Solving Equations Involving Parallel and Perpendicular Lines Examples


 Malcolm York
 2 years ago
 Views:
Transcription
1 Solving Equations Involving Parallel and Perpendicular Lines Examples. The graphs of y = x, y = x, and y = x + are lines that have the same slope. They are parallel lines. Definition of Parallel Lines In a plane, lines with the same slope are parallel lines. Also, all vertical lines are parallel.. Example Find the slope of a line parallel to the line whose equation is y x =. Parallel lines have the same slope. Find the slope of the line whose equation is y x =. To do so, write the equation in slopeintercept form (). y x = y = x + y = x + The slope of any line parallel to the given line is.. Example Find the slope of a line parallel to the line whose equation is y x = Parallel lines have the same slope. Find the slope of the line whose equation is y x =. To do so, write the equation in slopeintercept form (). y = x The slope of any line parallel to the given line is.
2 . Example Find an equation of the line that passes through (, 6) and is parallel to the line whose equation is y = x +. The slope is (notice that y = x + is in slopeintercept form. Use (, 6) and the slope to find the yintercept. 6 = ( )() + b 6 = 8 +b 0 = b Substitution Property 0 An equation of the line is y = x +. Thought Provoker What is the relationship between the x and yintercepts of parallel lines? If the intercepts are nonzero, the ratio of the x and yintercepts of a given line is equal to the ratio of the x and yintercepts of any line parallel to the given line. 6. Example Find an equation of the line that passes through (, ) and is parallel to y x = Rewrite y x = into slopeintercept form y = x + The slope of all parallel lines must be. Find b by substituting into slopeintercept form = ( ) + b b = 0 Therefore y = x + 0 must be the equation of a line passing through (, ) and parallel to y x =.
3 7. Example Find an equation of the line that passes through (, ) and is parallel to x + y = 6. Rewrite x + y = 6 into slopeintercept form y = The slope of all parallel lines must be. 6 x + Find b by substituting into slopeintercept form = ( ) + b b = Therefore y = x and parallel to x + y = must be the equation of a line passing through (, ) 8. The graphs of y = x + and y = x + 6 are lines that are perpendicular. Notice how their slopes are related: ( )( ) = The product of their slopes is 9. Definition of Perpendicular Lines In a plane, two nonvertical lines are perpendicular if and only if the product of their slopes is. Any vertical line is perpendicular to any horizontal line. 0. Here is a way to show that the slopes of any two nonvertical perpendicular lines in a plane have a product of. Consider a line that is neither vertical nor horizontal, with slope s r (see graph). Now consider rotating the line Notice that the slope r of the new line (see graph) is. The product of s r r the slopes of the two lines is ( )( ) =. s s
4 . Example Find the slope of a line perpendicular to the line whose equation is y x =. y x = y = x + Write equation in slopeintercept form. The slope of the given line is. (m) = m = Let m stand for the slope of the perpendicular line. The slope of any line perpendicular to the given line is. Example Find the slope of a line perpendicular to the line whose equation is x 7y = 6. x 7y = 6 6 y = x 7 7 Write equation in slopeintercept form. The slope is 7 (m) = 7 7 m = Let m stand for the slope of the perpendicular line. The slope of any line perpendicular to the given line is 7
5 . Example Find an equation of the line that passes through (, 6) and is perpendicular to the line whose equation is y = x +. The slope of the given line is. (m) = m = Use (, 6) and the slope 6 = ( )() + b = b Let m stand for the slope of the perpendicular line. to find the yintercept. The yintercept is. An equation of the line is y = x + This could be written x + y =. Example Find an equation of a line passing through (, ) and is perpendicular to x + y = 6. y = x + 6 The slope of the given line is. (m) = Let m stand for the slope of the perpendicular line. m = Use (, ) and the slope to find the yintercept. = ()( ) + b The yintercept is 0. 0 = b An equation of the line is y = x This could be written x y = 0
6 . Example Find an equation of a line that passes through (, ) and is perpendicular x + y =. y = x + The slope of the given line is (m) = m =. Let m stand for the slope of the perpendicular line. Use (, ) and the slope to find the yintercept. = ( )() + b = b The yintercept is An equation of the line is y = x. This could be written x y = 6. Thought Provoker Is it possible that two lines represented by 6x y = and x + y = 7 are perpendicular? Rewrite in slopeintercept form. 6x y = y = 6x + y = x + x + y = 7 y = x y = x + Yes. They are perpendicular. 6
7 Name: Date: Class: Solving Equations Involving Parallel and Perpendicular Lines Worksheet Find the slope of a line that is parallel and the slope of a line that is perpendicular to each line whose equation is given.. y = x +. y = x. x y = 8. y = x 8 6. x = y y x = 0 State whether the graphs of the following equations are parallel, perpendicular, or neither. 7. x + y = 8. x + y = x + y = 0 x y = 9. y = x 0. y + x = y = x y x =. x 8y = x 6y = 0. y + x = y + x =. x + y =. x + y = x + y = 7 x y = 7
8 Find an equation of the line that passes through each given point and is parallel to the line with the given equation.. (, ); y = x 6. (, ); y = x (, ); x + y = 8. (0, 0); x y = Find an equation of the line that passes through each given point and is perpendicular to the line with the given equation. 9. (, 0); y = x (, ); x + y = 7. (, 6); x + y =. (0, ); 6x y = Find the value of a for which the graph of the first equation is perpendicular to the graph of the second equation.. y = ax ; y = x. y = ax + ; y x = 7. y = a x 6; x + y = 6 6. y + ax = 8; y = x + 8
9 Name: Date: Class: Solving Equations Involving Parallel and Perpendicular Lines Worksheet Key Find the slope of a line that is parallel and the slope of a line that is perpendicular to each line whose equation is given.. y = x + Parallel slope = ; Perpendicular slope =. y = x y = x + Parallel slope = ; Perpendicular slope =. y = x 8 y = x Parallel slope = ; Perpendicular slope =. 6y x = 0 y = 6 x 6 Parallel slope = ; Perpendicular slope = 6. x y = y = x Parallel slope = ; Perpendicular slope = x = y y = x Parallel slope = ; Perpendicular slope = State whether the graphs of the following equations are parallel, perpendicular, or neither. y = x + Both have same slope. 7. x + y = y = x 0 Lines are parallel. x + y = 0 9
10 8. x + y = x y = y = x + y = x The product of the slopes is ()( ) = Lines are perpendicular. 9. y = x y = x Lines have same slope. y = x y = x Lines are parallel. 0. y + x = y x = y = x + y = x + The product of the slopes is ( )( ) = Lines are perpendicular.. x 8y = y = x 8 8 Neither x 6y = 0 y = x. y + x = y + x = y = x + y = x + Neither. x + y = x + y = 7 9 y = x y = x + Lines have same slope. Lines are parallel.. x + y = x y = y = x + 6 y = x The product of the slopes is ( )( ) = Lines are perpendicular. 0
11 Find an equation of the line that passes through each given point and is parallel to the line with the given equation.. (, ); y = x Use m = and (, ) to find b. = () + b b = 6 y = x 6 6. (, ); y = x + 6 Use m = and (, ) to find b. = () + b b = 0 y = x 7. (, ); x + y = x + y = y = x + Use m = and (, ); to find b. = ( ) + b 7 7 b = y = x + 8. (0, 0); x y = x y = y = x Use m = and (0, 0); to find b. 0 = (0) + b b = 0 y = x
12 Find an equation of the line that passes through each given point and is perpendicular to the line with the given equation. 9. (, 0); y = x + 7 m = For a perpendicular line use m = and (, 0) 0 = ( ) + b b = y = x + 0. (, ); x + y = 7 x + y = 7 y = m = 7 x + For a perpendicular line use m = and (, ) = () + b b = y = x +. (0, ); 6x y = 6x y = y = x m = For a perpendicular line use m = = b = (0) + b y = x and (0, )
13 . (, 6); x + y = x + y = y = x + m = For a perpendicular line use m = and (, 6) 6 = () + b b = y = x Find the value of a for which the graph of the first equation is perpendicular to the graph of the second equation.. y = ax ; y = x Rewrite y = x in slopeintercept form. y = x Compare slopes with y = ax. If a has a perpendicular slope then (a) = a =. y = ax + ; y x = 7 Rewrite y x = 7 in slopeintercept form. y = x + 7 Compare slopes with y = ax +. If a has a perpendicular slope then (a) = a =
14 . y = a x 6; x + y = 6 Rewrite x + y = 6 in slopeintercept form. a y = x + 6 Compare slopes with y = x 6. a If a has a perpendicular slope then ( ) = a = 6. y + ax = 8; y = x + Rewrite y + ax = 8 in slopeintercept form. a 8 y = x + Compare slopes with y = x +. a If a has a perpendicular slope then ( ) = a =
15 Student Name: Date: Solving Equations Involving Parallel and Perpendicular Lines Checklist. On questions thru 6, did the student find the slope of a parallel line? a. Yes (0 points) b. out of 6 ( points) c. out of 6 (0 points) d. out of 6 ( points) e. out of 6 (0 points) f. out of 6 ( points). On questions thru 6, did the student find the slope of a perpendicular line? a. Yes (0 points) b. out of 6 ( points) c. out of 6 (0 points) d. out of 6 ( points) e. out of 6 (0 points) f. out of 6 ( points). On questions 7 thru, did the student correctly determine the type of graphs? a. Yes (0 points) b. 7 out of 8 ( points) c. 6 out of 8 (0 points) d. out of 8 ( points) e. out of 8 (0 points) f. out of 8 ( points) g. out of 8 (0 points) h. out of 8 ( points). On questions thru 8, did the student find the equation of a parallel line correctly? a. Yes (0 points) b. out of ( points) c. out of (0 points) d. out of ( points). On questions 9 thru, did the student find the equation of a perpendicular line correctly? a. Yes (0 points) b. out of ( points) c. out of (0 points) d. out of ( points) 6. On questions thru 6, did the student solve for a correctly? a. Yes (0 points) b. out of ( points) c. out of (0 points) d. out of ( points) Total Number of Points
16 Name: Date: Class: NOTE: The sole purpose of this checklist is to aide the teacher in identifying students that need remediation. It is suggested that teacher s devise their own point range for determining grades. In addition, some students need remediation in specific areas. The following checklist provides a means for the teacher to assess which areas need addressing.. Does the student need remediation in content (finding the slope of a parallel and perpendicular line when given a linear equation) for questions thru 6? Yes No. Does the student need remediation in content (identifying parallel and perpendicular lines when given a pair of linear equations) for questions 7 thru? Yes No. Does the student need remediation in content (finding the equation of a parallel line when given a point and a linear equation) for questions thru 8? Yes No. Does the student need remediation in content (finding the equation of a perpendicular line when given a point and a linear equation) for questions 9 thru? Yes No. Does the student need remediation in content (finding the value of the constant term when given a perpendicular line) for questions thru 6? Yes No A B C D F 0 points and above 6 points and above points and above 96 points and above 9 points and below Sample Range of Points. 6
SlopeIntercept Form of a Linear Equation Examples
SlopeIntercept Form of a Linear Equation Examples. In the figure at the right, AB passes through points A(0, b) and B(x, y). Notice that b is the yintercept of AB. Suppose you want to find an equation
More informationSlopeIntercept Equation. Example
1.4 Equations of Lines and Modeling Find the slope and the y intercept of a line given the equation y = mx + b, or f(x) = mx + b. Graph a linear equation using the slope and the yintercept. Determine
More informationLinear Equations Review
Linear Equations Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The yintercept of the line y = 4x 7 is a. 7 c. 4 b. 4 d. 7 2. What is the yintercept
More informationWarm Up. Write an equation given the slope and yintercept. Write an equation of the line shown.
Warm Up Write an equation given the slope and yintercept Write an equation of the line shown. EXAMPLE 1 Write an equation given the slope and yintercept From the graph, you can see that the slope is
More informationSolving Systems of Equations Algebraically Examples
Solving Systems of Equations Algebraically Examples 1. Graphing a system of equations is a good way to determine their solution if the intersection is an integer. However, if the solution is not an integer,
More informationChapter 2 Section 4: Equations of Lines. 4.* Find the equation of the line with slope 4 3, and passing through the point (0,2).
Chapter Section : Equations of Lines Answers to Problems For problems , put our answers into slope intercept form..* Find the equation of the line with slope, and passing through the point (,0).. Find
More informationSection 3.4 The Slope Intercept Form: y = mx + b
SlopeIntercept Form: y = mx + b, where m is the slope and b is the yintercept Reminding! m = y x = y 2 y 1 x 2 x 1 Slope of a horizontal line is 0 Slope of a vertical line is Undefined Graph a linear
More information2.3 Writing Equations of Lines
. Writing Equations of Lines In this section ou will learn to use pointslope form to write an equation of a line use slopeintercept form to write an equation of a line graph linear equations using the
More informationSect The SlopeIntercept Form
Concepts # and # Sect.  The SlopeIntercept Form SlopeIntercept Form of a line Recall the following definition from the beginning of the chapter: Let a, b, and c be real numbers where a and b are not
More informationSection 1.1 Linear Equations: Slope and Equations of Lines
Section. Linear Equations: Slope and Equations of Lines Slope The measure of the steepness of a line is called the slope of the line. It is the amount of change in y, the rise, divided by the amount of
More information5 $75 6 $90 7 $105. Name Hour. Review Slope & Equations of Lines. STANDARD FORM: Ax + By = C. 1. What is the slope of a vertical line?
Review Slope & Equations of Lines Name Hour STANDARD FORM: Ax + By = C 1. What is the slope of a vertical line? 2. What is the slope of a horizontal line? 3. Is y = 4 the equation of a horizontal or vertical
More informationGraphing Linear Equations
Graphing Linear Equations I. Graphing Linear Equations a. The graphs of first degree (linear) equations will always be straight lines. b. Graphs of lines can have Positive Slope Negative Slope Zero slope
More informationName: Class: Date: Does the equation represent a direct variation? If so, find the constant of variation. c. yes; k = 5 3. c.
Name: Class: Date: Chapter 5 Test Multiple Choice Identify the choice that best completes the statement or answers the question. What is the slope of the line that passes through the pair of points? 1.
More informationWhat does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of y = mx + b.
PRIMARY CONTENT MODULE Algebra  Linear Equations & Inequalities T37/H37 What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of
More informationWriting the Equation of a Line in SlopeIntercept Form
Writing the Equation of a Line in SlopeIntercept Form SlopeIntercept Form y = mx + b Example 1: Give the equation of the line in slopeintercept form a. With yintercept (0, 2) and slope 9 b. Passing
More informationWrite the Equation of the Line Review
Connecting Algebra 1 to Advanced Placement* Mathematics A Resource and Strategy Guide Objective: Students will be assessed on their ability to write the equation of a line in multiple methods. Connections
More information1.3 LINEAR EQUATIONS IN TWO VARIABLES. Copyright Cengage Learning. All rights reserved.
1.3 LINEAR EQUATIONS IN TWO VARIABLES Copyright Cengage Learning. All rights reserved. What You Should Learn Use slope to graph linear equations in two variables. Find the slope of a line given two points
More informationIn this section, we ll review plotting points, slope of a line and different forms of an equation of a line.
Math 1313 Section 1.2: Straight Lines In this section, we ll review plotting points, slope of a line and different forms of an equation of a line. Graphing Points and Regions Here s the coordinate plane:
More informationPreCalculus III Linear Functions and Quadratic Functions
Linear Functions.. 1 Finding Slope...1 Slope Intercept 1 Point Slope Form.1 Parallel Lines.. Line Parallel to a Given Line.. Perpendicular Lines. Line Perpendicular to a Given Line 3 Quadratic Equations.3
More informationLinear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (1,3), (3,3), (2,3)}
Linear Equations Domain and Range Domain refers to the set of possible values of the xcomponent of a point in the form (x,y). Range refers to the set of possible values of the ycomponent of a point in
More information5. Equations of Lines: slope intercept & point slope
5. Equations of Lines: slope intercept & point slope Slope of the line m rise run SlopeIntercept Form m + b m is slope; b is intercept PointSlope Form m( + or m( Slope of parallel lines m m (slopes
More informationNumber of Solutions to Simultaneous Equations
Worksheet 3.5 Simultaneous Equations Section 1 Number of Solutions to Simultaneous Equations In maths we are sometimes confronted with two equations in two variables and we want to find out which values
More informationOrdered Pairs. Graphing Lines and Linear Inequalities, Solving System of Linear Equations. Cartesian Coordinates System.
Ordered Pairs Graphing Lines and Linear Inequalities, Solving System of Linear Equations Peter Lo All equations in two variables, such as y = mx + c, is satisfied only if we find a value of x and a value
More informationThe PointSlope Form
7. The PointSlope Form 7. OBJECTIVES 1. Given a point and a slope, find the graph of a line. Given a point and the slope, find the equation of a line. Given two points, find the equation of a line y Slope
More informationStudy Guide and Review  Chapter 4
State whether each sentence is true or false. If false, replace the underlined term to make a true sentence. 1. The yintercept is the ycoordinate of the point where the graph crosses the yaxis. The
More informationGRAPHING LINEAR EQUATIONS IN TWO VARIABLES
GRAPHING LINEAR EQUATIONS IN TWO VARIABLES The graphs of linear equations in two variables are straight lines. Linear equations may be written in several forms: SlopeIntercept Form: y = mx+ b In an equation
More informationSection 2.2 Equations of Lines
Section 2.2 Equations of Lines The Slope of a Line EXAMPLE: Find the slope of the line that passes through the points P(2,1) and Q(8,5). = 5 1 8 2 = 4 6 = 2 1 EXAMPLE: Find the slope of the line that passes
More informationThe slope m of the line passes through the points (x 1,y 1 ) and (x 2,y 2 ) e) (1, 3) and (4, 6) = 1 2. f) (3, 6) and (1, 6) m= 6 6
Lines and Linear Equations Slopes Consider walking on a line from left to right. The slope of a line is a measure of its steepness. A positive slope rises and a negative slope falls. A slope of zero means
More informationLines and Linear Equations. Slopes
Lines and Linear Equations Slopes Consider walking on a line from left to right. The slope of a line is a measure of its steepness. A positive slope rises and a negative slope falls. A slope of zero means
More informationx x y y Then, my slope is =. Notice, if we use the slope formula, we ll get the same thing: m =
Slope and Lines The slope of a line is a ratio that measures the incline of the line. As a result, the smaller the incline, the closer the slope is to zero and the steeper the incline, the farther the
More informationSection 1.4 Notes Page Linear Equations in Two Variables and Linear Functions., x
Section. Notes Page. Linear Equations in Two Variables and Linear Functions Slope Formula The slope formula is used to find the slope between two points ( x, y ) and ( ) x, y. x, y ) The slope is the vertical
More informationSection 1.10 Lines. The Slope of a Line
Section 1.10 Lines The Slope of a Line EXAMPLE: Find the slope of the line that passes through the points P(2,1) and Q(8,5). = 5 1 8 2 = 4 6 = 2 1 EXAMPLE: Find the slope of the line that passes through
More informationMath 10  Unit 7 Final Review  Coordinate Geometry
Class: Date: Math 10  Unit Final Review  Coordinate Geometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the slope of this line segment.
More informationTangent line of a circle can be determined once the tangent point or the slope of the line is known.
Worksheet 7: Tangent Line of a Circle Name: Date: Tangent line of a circle can be determined once the tangent point or the slope of the line is known. Straight line: an overview General form : Ax + By
More informationPreAP Algebra 2 Lesson 25 Graphing linear inequalities & systems of inequalities
Lesson 25 Graphing linear inequalities & systems of inequalities Objectives: The students will be able to  graph linear functions in slopeintercept and standard form, as well as vertical and horizontal
More informationExample SECTION 131. XAXIS  the horizontal number line. YAXIS  the vertical number line ORIGIN  the point where the xaxis and yaxis cross
CHAPTER 13 SECTION 131 Geometry and Algebra The Distance Formula COORDINATE PLANE consists of two perpendicular number lines, dividing the plane into four regions called quadrants XAXIS  the horizontal
More informationLinear Equations and Graphs
2.12.4 Linear Equations and Graphs Coordinate Plane Quadrants  The xaxis and yaxis form 4 "areas" known as quadrants. 1. I  The first quadrant has positive x and positive y points. 2. II  The second
More informationEQUATIONS and INEQUALITIES
EQUATIONS and INEQUALITIES Linear Equations and Slope 1. Slope a. Calculate the slope of a line given two points b. Calculate the slope of a line parallel to a given line. c. Calculate the slope of a line
More information5.1: Rate of Change and Slope
5.1: Rate of Change and Slope Rate of Change shows relationship between changing quantities. On a graph, when we compare rise and run, we are talking about steepness of a line (slope). You can use and
More informationAlgebra 1 Chapter 05 Review
Class: Date: Algebra 1 Chapter 05 Review Multiple Choice Identify the choice that best completes the statement or answers the question. Find the slope of the line that passes through the pair of points.
More informationChapter 4.1 Parallel Lines and Planes
Chapter 4.1 Parallel Lines and Planes Expand on our definition of parallel lines Introduce the idea of parallel planes. What do we recall about parallel lines? In geometry, we have to be concerned about
More informationMath 152 Rodriguez Blitzer 2.4 Linear Functions and Slope
Math 152 Rodriguez Blitzer 2.4 Linear Functions and Slope I. Linear Functions 1. A linear equation is an equation whose graph is a straight line. 2. A linear equation in standard form: Ax +By=C ex: 4x
More informationSolving Inequalities Examples
Solving Inequalities Examples 1. Joe and Katie are dancers. Suppose you compare their weights. You can make only one of the following statements. Joe s weight is less than Kate s weight. Joe s weight is
More informationMATH 105: Finite Mathematics 11: Rectangular Coordinates, Lines
MATH 105: Finite Mathematics 11: Rectangular Coordinates, Lines Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006 Outline 1 Rectangular Coordinate System 2 Graphing Lines 3 The Equation of
More informationPortable Assisted Study Sequence ALGEBRA IIA
SCOPE This course is divided into two semesters of study (A & B) comprised of five units each. Each unit teaches concepts and strategies recommended for intermediate algebra students. The first half of
More informationHow Many Solutions? Resource ID#: Primary Type: Formative Assessment
How Many Solutions? Resource ID#: 59692 Primary Type: Formative Assessment This document was generated on CPALMS  www.cpalms.org Students are asked to determine the number of solutions of each of four
More informationGRAPHING (2 weeks) Main Underlying Questions: 1. How do you graph points?
GRAPHING (2 weeks) The Rectangular Coordinate System 1. Plot ordered pairs of numbers on the rectangular coordinate system 2. Graph paired data to create a scatter diagram 1. How do you graph points? 2.
More informationSection 1.4 Graphs of Linear Inequalities
Section 1.4 Graphs of Linear Inequalities A Linear Inequality and its Graph A linear inequality has the same form as a linear equation, except that the equal symbol is replaced with any one of,,
More informationCOMPARING LINEAR AND NONLINEAR FUNCTIONS
1 COMPARING LINEAR AND NONLINEAR FUNCTIONS LEARNING MAP INFORMATION STANDARDS 8.F.2 Compare two s, each in a way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example,
More informationCreating Equations. Set 3: Writing Linear Equations Instruction. Student Activities Overview and Answer Key
Creating Equations Instruction Goal: To provide opportunities for students to develop concepts and skills related to writing linear equations in slopeintercept and standard form given two points and a
More informationAlgebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions.
Page 1 of 13 Review of Linear Expressions and Equations Skills involving linear equations can be divided into the following groups: Simplifying algebraic expressions. Linear expressions. Solving linear
More information4.1 & Linear Equations in SlopeIntercept Form
4.1 & 4.2  Linear Equations in SlopeIntercept Form SlopeIntercept Form: y = mx + b Ex 1: Write the equation of a line with a slope of 2 and a yintercept of 5. Ex 2:Write an equation of the line shown
More informationLecture 9: Lines. m = y 2 y 1 x 2 x 1
Lecture 9: Lines If we have two distinct points in the Cartesian plane, there is a unique line which passes through the two points. We can construct it by joining the points with a straight edge and extending
More informationPractice Test  Chapter 4. y = 2x 3. The slopeintercept form of a line is y = mx + b, where m is the slope, and b is the yintercept.
y = 2x 3. The slopeintercept form of a line is y = mx + b, where m is the slope, and b is the yintercept. Plot the yintercept (0, 3). The slope is. From (0, 3), move up 2 units and right 1 unit. Plot
More informationHelpsheet. Giblin Eunson Library LINEAR EQUATIONS. library.unimelb.edu.au/libraries/bee. Use this sheet to help you:
Helpsheet Giblin Eunson Library LINEAR EQUATIONS Use this sheet to help you: Solve linear equations containing one unknown Recognize a linear function, and identify its slope and intercept parameters Recognize
More informationDetermining Angle Measure with Parallel Lines Examples
Determining Angle Measure with Parallel Lines Examples 1. Using the figure at the right, review with students the following angles: corresponding, alternate interior, alternate exterior and consecutive
More informationStudents will use various media (computer, graphing calculator, paper and pencil) to graph/sketch linear equations.
Title: Lines, Lines, Everywhere!! A discovery/exploration lesson investigating equations of the form y = mx + b to see how the values of b and m affects the graph. Link to Outcomes: Communication/ Cooperation
More informationUse the graph shown to determine whether each system is consistent or inconsistent and if it is independent or dependent.
Use the graph shown to determine whether each system is consistent or inconsistent and if it is independent or dependent. y = 3x + 1 y = 3x + 1 The two equations intersect at exactly one point, so they
More informationWARM UP EXERCSE. 13 Linear Functions & Straight lines
WARM UP EXERCSE A company makes and sells inline skates. The pricedemand function is p (x) = 190 0.013(x 10) 2. Describe how the graph of function p can be obtained from one of the library functions.
More informationUnit 5: Coordinate Geometry Practice Test
Unit 5: Coordinate Geometry Practice Test Math 10 Common Name: Block: Please initial this box to indicate you carefully read over your test and checked your work for simple mistakes. What I can do in this
More informationThe Parabola and the Circle
The Parabola and the Circle The following are several terms and definitions to aid in the understanding of parabolas. 1.) Parabola  A parabola is the set of all points (h, k) that are equidistant from
More informationAlgebra 1 Chapter 3 Vocabulary. equivalent  Equations with the same solutions as the original equation are called.
Chapter 3 Vocabulary equivalent  Equations with the same solutions as the original equation are called. formula  An algebraic equation that relates two or more reallife quantities. unit rate  A rate
More informationA synonym is a word that has the same or almost the same definition of
SlopeIntercept Form Determining the Rate of Change and yintercept Learning Goals In this lesson, you will: Graph lines using the slope and yintercept. Calculate the yintercept of a line when given
More informationLines, Lines, Lines!!! SlopeIntercept Form ~ Lesson Plan
Lines, Lines, Lines!!! SlopeIntercept Form ~ Lesson Plan I. Topic: SlopeIntercept Form II. III. Goals and Objectives: A. The student will write an equation of a line given information about its graph.
More informationMidterm 1. Solutions
Stony Brook University Introduction to Calculus Mathematics Department MAT 13, Fall 01 J. Viro October 17th, 01 Midterm 1. Solutions 1 (6pt). Under each picture state whether it is the graph of a function
More informationWhat students need to know for... ALGEBRA II
What students need to know for... ALGEBRA II 20152016 NAME Students expecting to take Algebra II at Cambridge Rindge & Latin School should demonstrate the ability to... General: o Keep an organized notebook
More informationMath 155 (DoVan) Exam 1 Review (Sections 3.1, 3.2, 5.1, 5.2, Chapters 2 & 4)
Chapter 2: Functions and Linear Functions 1. Know the definition of a relation. Math 155 (DoVan) Exam 1 Review (Sections 3.1, 3.2, 5.1, 5.2, Chapters 2 & 4) 2. Know the definition of a function. 3. What
More informationLesson 9: Graphing Standard Form Equations Lesson 2 of 2. Example 1
Lesson 9: Graphing Standard Form Equations Lesson 2 of 2 Method 2: Rewriting the equation in slope intercept form Use the same strategies that were used for solving equations: 1. 2. Your goal is to solve
More informationLINEAR FUNCTIONS. Form Equation Note Standard Ax + By = C A and B are not 0. A > 0
LINEAR FUNCTIONS As previousl described, a linear equation can be defined as an equation in which the highest eponent of the equation variable is one. A linear function is a function of the form f ( )
More informationAlgebra I Pacing Guide Days Units Notes 9 Chapter 1 ( , )
Algebra I Pacing Guide Days Units Notes 9 Chapter 1 (1.11.4, 1.61.7) Expressions, Equations and Functions Differentiate between and write expressions, equations and inequalities as well as applying order
More informationSection summaries. d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2. 1 + y 2. x1 + x 2
Chapter 2 Graphs Section summaries Section 2.1 The Distance and Midpoint Formulas You need to know the distance formula d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 and the midpoint formula ( x1 + x 2, y ) 1 + y 2
More informationThe Perpendicular Bisector of a Segment
Check off the steps as you complete them: The Perpendicular Bisector of a Segment Open a Geometry window in Geogebra. Use the segment tool of draw AB. Under the point tool, select Midpoint of Center, and
More informationHIBBING COMMUNITY COLLEGE COURSE OUTLINE
HIBBING COMMUNITY COLLEGE COURSE OUTLINE COURSE NUMBER & TITLE:  Beginning Algebra CREDITS: 4 (Lec 4 / Lab 0) PREREQUISITES: MATH 0920: Fundamental Mathematics with a grade of C or better, Placement Exam,
More informationWorksheet A5: Slope Intercept Form
Name Date Worksheet A5: Slope Intercept Form Find the Slope of each line below 1 3 Y           Graph the lines containing the point below, then find their slopes from counting on the graph!.
More informationI. Model Problems. II. Practice III. Challenge Problems VI. Answer Key
www.mathworksheetsgo.com On Twitter: twitter.com/mathprintables I. Model Problems. II. Practice III. Challenge Problems VI. Answer Key Web Resources Equations of Lines www.mathwarehouse.com/algebra/linear_equation/equationofalineformula.php
More informationVocabulary Words and Definitions for Algebra
Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms
More informationGeometry 1. Unit 3: Perpendicular and Parallel Lines
Geometry 1 Unit 3: Perpendicular and Parallel Lines Geometry 1 Unit 3 3.1 Lines and Angles Lines and Angles Parallel Lines Parallel lines are lines that are coplanar and do not intersect. Some examples
More informationSolving Systems of Linear Equations Graphing
Solving Systems of Linear Equations Graphing Outcome (learning objective) Students will accurately solve a system of equations by graphing. Student/Class Goal Students thinking about continuing their academic
More informationFinal Graphing Practice #1
Final Graphing Practice #1 Beginning Algebra / Math 100 Fall 2013 506 (Prof. Miller) Student Name/ID: Instructor Note: Assignment: Set up a tutoring appointment with one of the campus tutors or with me.
More informationName: Date: Block: Midterm Exam Review Sheet 1
Name: Date: Block: Midterm Exam Review Sheet 1 Chapter 1 1. Write a variable expression for 2. Simplify: 8 3 2 4 seven divided by the sum of x and five 3. Write an algebraic expression for 4. Write an
More informationSection 1.8 Coordinate Geometry
Section 1.8 Coordinate Geometry The Coordinate Plane Just as points on a line can be identified with real numbers to form the coordinate line, points in a plane can be identified with ordered pairs of
More informationAlgebra I: Strand 2. Linear Functions; Topic 2. Formalizing Slope and yintercept; Task
1 TASK : DESCRIBE STACKING CUPS Solutions Make a scatter plot of the data. Write a symbolic function rule and a verbal description of the situation. 1. 1 1 1 Number of Cups 0.5 1 6.0 2 8.5 11.0 2.5 2.5
More informationDesign a Brochure Algebra 2 Project Linear Equations and Inequalities
Design a Brochure Algebra 2 Project Linear Equations and Inequalities Purpose: For this project, you will be working as a group of two to design a trifold brochure or an alternate display that will summarize
More informationAlgebra. Indiana Standards 1 ST 6 WEEKS
Chapter 1 Lessons Indiana Standards  11 Variables and Expressions  12 Order of Operations and Evaluating Expressions  13 Real Numbers and the Number Line  14 Properties of Real Numbers  15 Adding
More informationGraphing Equations. with Color Activity
Graphing Equations with Color Activity Students must rewrite equations into slope intercept form and then graph them on a coordinate plane. 2011 Lindsay Perro Name Date Between The Lines Rewrite each
More informationMA.8.A.1.2 Interpret the slope and the x and yintercepts when graphing a linear equation for a realworld problem. Constant Rate of Change/Slope
MA.8.A.1.2 Interpret the slope and the x and yintercepts when graphing a linear equation for a realworld problem Constant Rate of Change/Slope In a Table Relationships that have straightlined graphs
More informationExam 2 Review. 3. How to tell if an equation is linear? An equation is linear if it can be written, through simplification, in the form.
Exam 2 Review Chapter 1 Section1 Do You Know: 1. What does it mean to solve an equation? To solve an equation is to find the solution set, that is, to find the set of all elements in the domain of the
More informationModuMath Algebra Lessons
ModuMath Algebra Lessons Program Title 1 Getting Acquainted With Algebra 2 Order of Operations 3 Adding & Subtracting Algebraic Expressions 4 Multiplying Polynomials 5 Laws of Algebra 6 Solving Equations
More information2.1 Equations of Lines
Section 2.1 Equations of Lines 1 2.1 Equations of Lines The SlopeIntercept Form Recall the formula for the slope of a line. Let s assume that the dependent variable is and the independent variable is
More informationUnit III Practice Questions
Unit III Practice Questions 1. Write the ordered pair corresponding to each point plotted below. A F B E D C 2. Determine if the ordered pair ( 1, 2) is a solution of 2x + y = 4. Explain how you know.
More informationSection 3.2. Graphing linear equations
Section 3.2 Graphing linear equations Learning objectives Graph a linear equation by finding and plotting ordered pair solutions Graph a linear equation and use the equation to make predictions Vocabulary:
More informationCourse Name: Course Code: ALEKS Course: Instructor: Course Dates: Course Content: Textbook: Dates Objective Prerequisite Topics
Course Name: MATH 1204 Fall 2015 Course Code: N/A ALEKS Course: College Algebra Instructor: Master Templates Course Dates: Begin: 08/22/2015 End: 12/19/2015 Course Content: 271 Topics (261 goal + 10 prerequisite)
More information2 Reason: This is harder. I'll give an argument in an Addendum to this handout.
LINES Slope The slope of a nonvertical line in a coordinate plane is defined as follows: Let P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) be any two points on the line. Then slope of the line = y 2 y 1 change in
More informationSlopeIntercept Quiz. Name: Class: Date: 1. Graph the line with the slope 1 and yintercept 3. a. c. b. d.
Name: Class: Date: ID: A SlopeIntercept Quiz 1. Graph the line with the slope 1 and yintercept 3. a. c. b. d.. Write the equation that describes the line with slope = and yintercept = 3 a. x + y = 3
More informationGrade 10 Applied Math Unit 3: Linear Equations Lesson: Date: Completed Level Lesson 1: Coordinates Review Lesson 2: Constructing Tables and Sketching
Grade 10 Applied Math Unit 3: Linear Equations Lesson: Date: Completed Level Lesson 1: Coordinates Review Lesson 2: Constructing Tables and Sketching Graphs Lesson 3: Interpreting Lines Lesson 4: Write
More information2.1 Algebraic Expressions and Combining like Terms
2.1 Algebraic Expressions and Combining like Terms Evaluate the following algebraic expressions for the given values of the variables. 3 3 3 Simplify the following algebraic expressions by combining like
More informationLesson 8.3 Exercises, pages
Lesson 8. Eercises, pages 57 5 A. For each function, write the equation of the corresponding reciprocal function. a) = 5  b) = 5 c) =  d) =. Sketch broken lines to represent the vertical and horizontal
More informationLecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20
Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding
More information) represents the original function, will a, r 1
Transformations of Quadratic Functions Focus on Content: Download Problem Sets Problem Set #1 1. In the graph below, the quadratic function displayed on the right has been reflected over the yaxis producing
More informationActivity 6 Graphing Linear Equations
Activity 6 Graphing Linear Equations TEACHER NOTES Topic Area: Algebra NCTM Standard: Represent and analyze mathematical situations and structures using algebraic symbols Objective: The student will be
More information