# Sect The Slope-Intercept Form

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Concepts # and # Sect. - The Slope-Intercept Form Slope-Intercept 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 both zero. Then an equation that can be written in the form: ax + by = c is called a linear equation in two variables If a, b, and c happen to integers with a > 0, then we call this the standard form of a linear equation. A linear equation in two variables is said to be written in standard form if it is in the form: Ax + By = C, where A, B, and C are integers and both A and B cannot be zero. We also saw that if the linear equation is solved for y, the constant term was the y-coordinate of the y-intercept. In other words, if y = mx + b, then 0, b) is the y-intercept. Now, let us find the slope of the line. The y- intercept, 0, b), is one point on the line. If we let x =, then y = m) + b = m + b. So,, m + b) is a second point on the line. The slope is equal to y y x x = m+b b 0 = m = m. Thus, the coefficient of the x-term is m. Slope-intercept form A linear equation in two variables is said to be written in slope-intercept form if it is in the form y = mx + b where m is the slope of the line and the point 0, b) is the y-intercept. Given the graph below, find a) the slope, b) y-intercept, and c) the equation of the line: Ex. Ex.

2 a) The graph cross the a) The graph cross the at, so the y-intercept is at, so the y-intercept is 0, ). 0, ). b) Moving from the point b) Moving from the point 0, ) to, 0), we have to 0, ) to, ), we have to rise unit and run units. So, fall units and run unit. So, the slope is "rise" c) Since m = =. the slope is "rise" = =. and b =, c) Since m = and b =, the equation is y = x. the equation is y = x +. Ex. Ex. a) The graph cross the a) The graph cross the at, so the y-intercept is at, so the y-intercept is 0, ). 0, ). b) Moving from the point b) Moving from the point 0, ) to, 6), we have to 0, ) to 6, ), we have to fall units and run units. So, rise unit and run 6 units. So, the slope is "rise" = =. the slope is "rise" c) Since m = and b =, c) Since m = 6 the equation is y = x. the equation is y = 6 x +. = 6. and b =, We can also go backwards to find the slope. In example #, if we move from 0, ) to, ), we would rise units and run units backwards, So, our slope would be "rise" went from 0, ) to 6, ), we would fall unit and run 6 units backwards. So, our slope would be "rise" = =. Likewise, in example #, if we = 6 = 6.

3 5 Ex. 5 Ex. 6 a) The graph cross the a) The graph does not cross the at, so the y-intercept is, so there is no y-intercept. 0, ). b) This is a horizontal line so, b) This is a vertical line so, m = 0. m is undefined. c) The equation of a horizontal c) The equation of a vertical line line is in the form y = #. Since is in the form x = #. Since the line the line crosses the at, crosses the at, then the then the equation is y =. equation is x =. Find the slope and y-intercept and sketch the graph: Ex. 7 x + y = 5 First solve the equation for y: x + y = 5 + x = + x y = x 5 The slope is = = "rise" and the y-intercept is 0, 5). Plot the point 0, 5). Then from that point rise units and run unit to get another point. From that new point, rise another units and run more unit to get the third point. Now, draw the graph. 5 y - axis x - axis

4 6 Ex. 8 x 6y = First solve the equation for y: x 6y = x = x 6y = x y = x The slope is = "rise" and the y-intercept is 0, ). Plot the point 0, ). Then from that point rise unit and run units to get another point. From that new point, rise another unit and run more units to get the third point. Now, draw the graph. y - axis x - axis Ex. 9 8x + y = First solve the equation for y: 8x + y = 8x = 8x y = 8x + y = 8 x + 8 The slope is 8 = 8 and the y-intercept is 0, 8). Plot the point 0, 8). Then from that point fall 8 units and run units to get another point. From that new point fall another 8 units and run more units to get the third point. Now, draw the graph. = "rise" y - axis x - axis - Concept # Determining Whether Two Lines are Parallel, Perpendicular, or Neither

5 7 Determine if the lines are parallel, perpendicular, or neither. Ex. 0 8x 7y = 6 Ex. x = y 8y = 7x + x + y = 5 First, solve each equation First, solve each equation for y to find the slope. for y to find the slope. 8x 7y = 6 x = y 8x = 8x y = x 7y = 8x + 6 m = 7 7 x + y = 5 y = 8 7 x 6 7 x = x m = 8 7 y = x + 5 8y = 7x + m = 8 8 y = 7 8 x + 8 But, m m, so they are not m = 7 8 parallel. Also, m m = ) Since m m = ) = 6, so they are not =, the lines are perpendicular. There the lines perpendicular. are neither. Ex. 9 x 6 y =.x 0.9y =.8 First, solve each equation for y to find the slope. 8 9 x ) 8 6 y ) = 8) 0.x) 00.9y) = 0.8) x ) y ) = 8) x 9y = 8 x y = 8 x = x x = x 9y = x + 8 y = x y = x 6 y = x m = Since m = m, then the lines are parallel. m =

6 8 Concept # Writing the Equation of the Line Given Its Slope and y-intercept Use the given information to write the equation of the line: Ex. The slope of the line is and it passes through 0, ). 8 m = and 0, b) = 0, ) which implies b =. 8 Plugging into y = mx + b, we get: y = 8 x So, the equation is y = 8 x. Ex. The slope of the line is and it passes through 0, ) m = and 0, b) = 0, ) which implies b =. Plugging into y = mx + b, we get: y = x + So, the equation is y = x +. Ex. 5 The slope of the line is 0 and it passes through, 5). m = 0, but we do not have a y-intercept. A line with a slope of 0 is a horizontal line. Recall that a horizontal is in the form of y = constant. Since it has to pass through the point, 5), then y has to be 5. So, the equation is y = 5. Ex. 6 The slope of the line is undefined and it passes through, 5). m is undefined and we do not have a y-intercept. A line with a slope that is undefined is a vertical line. Recall that a vertical is in the form of x = constant. Since it has to pass through the point, 5), then x has to be. So, the equation is x =.

### Section 3.4 The Slope Intercept Form: y = mx + b

Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept 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

### Graphing 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

### Section 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

### Linear Equations Review

Linear Equations Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The y-intercept of the line y = 4x 7 is a. 7 c. 4 b. 4 d. 7 2. What is the y-intercept

### Slope-Intercept 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 y-intercept. Determine

### Warm Up. Write an equation given the slope and y-intercept. Write an equation of the line shown.

Warm Up Write an equation given the slope and y-intercept Write an equation of the line shown. EXAMPLE 1 Write an equation given the slope and y-intercept From the graph, you can see that the slope is

### 2.3 Writing Equations of Lines

. Writing Equations of Lines In this section ou will learn to use point-slope form to write an equation of a line use slope-intercept form to write an equation of a line graph linear equations using the

### Linear Equations and Graphs

2.1-2.4 Linear Equations and Graphs Coordinate Plane Quadrants - The x-axis and y-axis form 4 "areas" known as quadrants. 1. I - The first quadrant has positive x and positive y points. 2. II - The second

### The 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

### Lines 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

### The Point-Slope Form

7. The Point-Slope 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

### Linear 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 x-component of a point in the form (x,y). Range refers to the set of possible values of the y-component of a point in

### In 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:

### MATH 105: Finite Mathematics 1-1: Rectangular Coordinates, Lines

MATH 105: Finite Mathematics 1-1: Rectangular Coordinates, Lines Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006 Outline 1 Rectangular Coordinate System 2 Graphing Lines 3 The Equation of

### Name: 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.

### Solving Equations Involving Parallel and Perpendicular Lines Examples

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

### 5 \$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

### GRAPHING 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: Slope-Intercept Form: y = mx+ b In an equation

### 4.1 & Linear Equations in Slope-Intercept Form

4.1 & 4.2 - Linear Equations in Slope-Intercept Form Slope-Intercept Form: y = mx + b Ex 1: Write the equation of a line with a slope of -2 and a y-intercept of 5. Ex 2:Write an equation of the line shown

### Chapter 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

### Math 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

### Graphing - Slope-Intercept Form

2.3 Graphing - Slope-Intercept Form Objective: Give the equation of a line with a known slope and y-intercept. When graphing a line we found one method we could use is to make a table of values. However,

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

### Writing the Equation of a Line in Slope-Intercept Form

Writing the Equation of a Line in Slope-Intercept Form Slope-Intercept Form y = mx + b Example 1: Give the equation of the line in slope-intercept form a. With y-intercept (0, 2) and slope -9 b. Passing

### 5.1: 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

### 5.1 Writing Linear Equations in Slope-Intercept Form. 1. Use slope-intercept form to write an equation of a line.

5.1 Writing Linear Equations in Slope-Intercept Form Objectives 1. Use slope-intercept form to write an equation of a line. 2. Model a real-life situation with a linear function. Key Terms Slope-Intercept

### Slope-Intercept Form of a Linear Equation Examples

Slope-Intercept 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 y-intercept of AB. Suppose you want to find an equation

### Section 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

### LINEAR 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 ( )

### EQUATIONS 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

### Study 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 y-intercept is the y-coordinate of the point where the graph crosses the y-axis. The

### 2.1 Equations of Lines

Section 2.1 Equations of Lines 1 2.1 Equations of Lines The Slope-Intercept Form Recall the formula for the slope of a line. Let s assume that the dependent variable is and the independent variable is

### Section 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

### Pre-Calculus 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

### Ordered 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

### Write 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

### COMPARING 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,

### WARM UP EXERCSE. 1-3 Linear Functions & Straight lines

WARM UP EXERCSE A company makes and sells inline skates. The price-demand 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.

### Equations of Lines Derivations

Equations of Lines Derivations If you know how slope is defined mathematically, then deriving equations of lines is relatively simple. We will start off with the equation for slope, normally designated

### 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 y = mx + b.

PRIMARY CONTENT MODULE Algebra - Linear Equations & Inequalities T-37/H-37 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

### Section 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

### Answer Key Building Polynomial Functions

Answer Key Building Polynomial Functions 1. What is the equation of the linear function shown to the right? 2. How did you find it? y = ( 2/3)x + 2 or an equivalent form. Answers will vary. For example,

### CHAPTER 2: POLYNOMIAL AND RATIONAL FUNCTIONS

CHAPTER 2: POLYNOMIAL AND RATIONAL FUNCTIONS 2.01 SECTION 2.1: QUADRATIC FUNCTIONS (AND PARABOLAS) PART A: BASICS If a, b, and c are real numbers, then the graph of f x = ax2 + bx + c is a parabola, provided

### Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 2014-2015 school year.

Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 2014-2015 school year. Goal The goal of the summer math program is to help students

### Lecture 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

### GRAPHING (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.

### Coordinate Plane, Slope, and Lines Long-Term Memory Review Review 1

Review. What does slope of a line mean?. How do you find the slope of a line? 4. Plot and label the points A (3, ) and B (, ). a. From point B to point A, by how much does the y-value change? b. From point

### MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem. Constant Rate of Change/Slope

MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem Constant Rate of Change/Slope In a Table Relationships that have straight-lined graphs

### Chapter 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

### Practice Test - Chapter 4. y = 2x 3. The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept.

y = 2x 3. The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept. Plot the y-intercept (0, 3). The slope is. From (0, 3), move up 2 units and right 1 unit. Plot

### Math 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.

### Creating 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 slope-intercept and standard form given two points and a

### x 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

### Section 2.1 Rectangular Coordinate Systems

P a g e 1 Section 2.1 Rectangular Coordinate Systems 1. Pythagorean Theorem In a right triangle, the lengths of the sides are related by the equation where a and b are the lengths of the legs and c is

### Math 113 Review for Exam I

Math 113 Review for Exam I Section 1.1 Cartesian Coordinate System, Slope, & Equation of a Line (1.) Rectangular or Cartesian Coordinate System You should be able to label the quadrants in the rectangular

### Pre-AP Algebra 2 Lesson 2-5 Graphing linear inequalities & systems of inequalities

Lesson 2-5 Graphing linear inequalities & systems of inequalities Objectives: The students will be able to - graph linear functions in slope-intercept and standard form, as well as vertical and horizontal

### Lecture 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

### Algebra I Pacing Guide Days Units Notes 9 Chapter 1 ( , )

Algebra I Pacing Guide Days Units Notes 9 Chapter 1 (1.1-1.4, 1.6-1.7) Expressions, Equations and Functions Differentiate between and write expressions, equations and inequalities as well as applying order

### Algebra 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 real-life quantities. unit rate - A rate

### Building Polynomial Functions

Building Polynomial Functions NAME 1. What is the equation of the linear function shown to the right? 2. How did you find it? 3. The slope y-intercept form of a linear function is y = mx + b. If you ve

### Graphing - Parallel and Perpendicular Lines

. Graphing - Parallel and Perpendicular Lines Objective: Identify the equation of a line given a parallel or perpendicular line. There is an interesting connection between the slope of lines that are parallel

### The 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

### Slope-Intercept Quiz. Name: Class: Date: 1. Graph the line with the slope 1 and y-intercept 3. a. c. b. d.

Name: Class: Date: ID: A Slope-Intercept Quiz 1. Graph the line with the slope 1 and y-intercept 3. a. c. b. d.. Write the equation that describes the line with slope = and y-intercept = 3 a. x + y = 3

### Pre-AP Algebra 2 Unit 3 Lesson 1 Quadratic Functions

Unit 3 Lesson 1 Quadratic Functions Objectives: The students will be able to Identify and sketch the quadratic parent function Identify characteristics including vertex, axis of symmetry, x-intercept,

### Unit 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

### Packet: Lines (Part 1) Standards covered:

Packet: Lines (Part 1) Standards covered: *(2)MA.912.A.3.8 Graph a line given any of the following information: a table of values, the x and y- intercepts, two points, the slope and a point, the equation

### Intro to Linear Equations Algebra 6.0

Intro to Linear Equations Algebra 6.0 Linear Equations: y x 7 y x 5 x y Linear Equations generally contain two variables: x and y. In a linear equation, y is called the dependent variable and x is the

### Algebraic 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

### Example SECTION 13-1. X-AXIS - the horizontal number line. Y-AXIS - the vertical number line ORIGIN - the point where the x-axis and y-axis cross

CHAPTER 13 SECTION 13-1 Geometry and Algebra The Distance Formula COORDINATE PLANE consists of two perpendicular number lines, dividing the plane into four regions called quadrants X-AXIS - the horizontal

### Course 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)

### A synonym is a word that has the same or almost the same definition of

Slope-Intercept Form Determining the Rate of Change and y-intercept Learning Goals In this lesson, you will: Graph lines using the slope and y-intercept. Calculate the y-intercept of a line when given

### What are the x- and y-intercepts?

.: Graphing Linear Functions STARTER. What does it mean to INTERCEPT a pass in football? The path of the defender crosses the path of the thrown football. In algebra, what are - and -intercepts? What are

### MATH 111: EXAM 02 SOLUTIONS

MATH 111: EXAM 02 SOLUTIONS BLAKE FARMAN UNIVERSITY OF SOUTH CAROLINA Answer the questions in the spaces provided on the question sheets and turn them in at the end of the class period Unless otherwise

### 2.7. The straight line. Introduction. Prerequisites. Learning Outcomes. Learning Style

The straight line 2.7 Introduction Probably the most important function and graph that you will use are those associated with the straight line. A large number of relationships between engineering variables

### Algebra. Indiana Standards 1 ST 6 WEEKS

Chapter 1 Lessons Indiana Standards - 1-1 Variables and Expressions - 1-2 Order of Operations and Evaluating Expressions - 1-3 Real Numbers and the Number Line - 1-4 Properties of Real Numbers - 1-5 Adding

### Objectives: To graph exponential functions and to analyze these graphs. None. The number A can be any real constant. ( A R)

CHAPTER 2 LESSON 2 Teacher s Guide Graphing the Eponential Function AW 2.6 MP 2.1 (p. 76) Objectives: To graph eponential functions and to analyze these graphs. Definition An eponential function is a function

### Beginning of the Semester To-Do List

Beginning of the Semester To-Do List Set up your account at https://casa.uh.edu/ Read the Math 13xx Departmental Course Policies Take Course Policies Quiz until your score is 100%. You can find it on the

### Lines, Lines, Lines!!! Slope-Intercept Form ~ Lesson Plan

Lines, Lines, Lines!!! Slope-Intercept Form ~ Lesson Plan I. Topic: Slope-Intercept Form II. III. Goals and Objectives: A. The student will write an equation of a line given information about its graph.

### Name: 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

### 5. Equations of Lines: slope intercept & point slope

5. Equations of Lines: slope intercept & point slope Slope of the line m rise run Slope-Intercept Form m + b m is slope; b is -intercept Point-Slope Form m( + or m( Slope of parallel lines m m (slopes

### Section 7.1 Solving Linear Systems by Graphing. System of Linear Equations: Two or more equations in the same variables, also called a.

Algebra 1 Chapter 7 Notes Name Section 7.1 Solving Linear Systems by Graphing System of Linear Equations: Two or more equations in the same variables, also called a. Solution of a System of Linear Equations:

### Practice Problems for Exam 1 Math 140A, Summer 2014, July 2

Practice Problems for Exam 1 Math 140A, Summer 2014, July 2 Name: INSTRUCTIONS: These problems are for PRACTICE. For the practice exam, you may use your book, consult your classmates, and use any other

### Alex and Morgan were asked to graph the equation y = 2x + 1

Which is better? Ale and Morgan were asked to graph the equation = 2 + 1 Ale s make a table of values wa Morgan s use the slope and -intercept wa First, I made a table. I chose some -values, then plugged

### Portable 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

### Chapter 6 Notes. Section 6.1 Solving One-Step Linear Inequalities

Chapter 6 Notes Name Section 6.1 Solving One-Step Linear Inequalities Graph of a linear Inequality- the set of all points on a number line that represent all solutions of the inequality > or < or circle

### CHAPTER 1 Linear Equations

CHAPTER 1 Linear Equations 1.1. Lines The rectangular coordinate system is also called the Cartesian plane. It is formed by two real number lines, the horizontal axis or x-axis, and the vertical axis or

### Section 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,,

### 2x - y 4 y -3x - 6 y < 2x 5x - 3y > 7

DETAILED SOLUTIONS AND CONCEPTS GRAPHICAL REPRESENTATION OF LINEAR INEQUALITIES IN TWO VARIABLES Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu.

### Homework #1 Solutions

Homework #1 Solutions Problems Section 1.1: 8, 10, 12, 14, 16 Section 1.2: 2, 8, 10, 12, 16, 24, 26 Extra Problems #1 and #2 1.1.8. Find f (5) if f (x) = 10x x 2. Solution: Setting x = 5, f (5) = 10(5)

### Aim: How do we find the slope of a line? Warm Up: Go over test. A. Slope -

Aim: How do we find the slope of a line? Warm Up: Go over test A. Slope - Plot the points and draw a line through the given points. Find the slope of the line.. A(-5,4) and B(4,-3) 2. A(4,3) and B(4,-6)

### 1 Functions, Graphs and Limits

1 Functions, Graphs and Limits 1.1 The Cartesian Plane In this course we will be dealing a lot with the Cartesian plane (also called the xy-plane), so this section should serve as a review of it and its

### Pre-Calculus Review Lesson 1 Polynomials and Rational Functions

If a and b are real numbers and a < b, then Pre-Calculus Review Lesson 1 Polynomials and Rational Functions For any real number c, a + c < b + c. For any real numbers c and d, if c < d, then a + c < b

### Section 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:

### Rational Functions ( )

Rational Functions A rational function is a function of the form r P Q where P and Q are polynomials. We assume that P() and Q() have no factors in common, and Q() is not the zero polynomial. The domain

### Students 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

### Worksheet 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!.

### Plot the following two points on a graph and draw the line that passes through those two points. Find the rise, run and slope of that line.

Objective # 6 Finding the slope of a line Material: page 117 to 121 Homework: worksheet NOTE: When we say line... we mean straight line! Slope of a line: It is a number that represents the slant of a line

### 3.3. Solving Polynomial Equations. Introduction. Prerequisites. Learning Outcomes

Solving Polynomial Equations 3.3 Introduction Linear and quadratic equations, dealt within Sections 3.1 and 3.2, are members of a class of equations, called polynomial equations. These have the general