Lines, Lines, Lines!!! Horizontal and Vertical Lines ~ Lesson Plan
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1 Lines, Lines, Lines!!! Horizontal and Vertical Lines ~ Lesson Plan I. Topic: Horizontal and Vertical Lines II. III. Goals and Objectives: A. The students will understand the difference between horizontal and vertical lines. B. The students will graph the different type of lines. C. The students will find the equation of horizontal and vertical lines. Massachusetts Learning Standards: 1. 8.P.3 Demonstrate an understanding of the identity (-x)(-y) = xy. Using this identity to simplify algebraic expressions P.5 Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems P.6 Identify the roles of variables within an equation, e.g., y = mx + b, expressing y as a function of x with parameters m and b P.7 Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graph P.2 Demonstrate an understanding of the relationship between various representations of a line. Determine a line s slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or geometric description of the line, e.g, by using the point-slope or slope y-intercept formulas. Explain the significance of a positive, negative, zero, or undefined slope. Atlantic Union Conference Teacher Bulletin Page 1 of 20
2 IV. Materials: A. Whiteboard with dry-erase markers (Blackboard with chalk could also be used.) B. Ruler. C. Pencils. D. Calculator. E. Graphing Paper. F. Horizontal and Vertical Lines Worksheets (Practice Worksheet, Quiz Worksheet). V. Presentation Outline: A. Introduction. "Understanding the Nature of Horizontal and Vertical Lines." I. Formulas II. Definitions B. Write an equation for a Horizontal Line. Examples C. Write an equation for a Vertical Line. Examples D. Graph the given Horizontal and Vertical Lines Examples VI. Presentation: A. Presentation Notes B. Power Point Presentation VII. Independent Practice: Horizontal and Vertical Lines Worksheet A. Class work: #1-9 Odds B. Homework: # 2-10 Even C. Due the next day. VIII. Topic Assessment: Horizontal and Vertical Lines Quiz A. Answer questions from homework. B. 5-Question Quiz: minutes C. 10-Question Quiz: minutes. Atlantic Union Conference Teacher Bulletin Page 2 of 20
3 Lines, Lines, Lines!!! ~ Equations For Horizontal and Vertical Lines Introduction Horizontal and Vertical lines are by far the easiest to graph. Also their equations are easy to write. With a very basic understanding of points and the coordinate plane, anyone can graph these lines. Remember that every time we talked about Horizontal lines we looked at the horizon; we looked at the line the sun dives into. Horizontal lines go indefinitely from left to right. Vertical lines are the exact opposite of horizontal lines. You don't stand horizontally; you stand vertically. Vertical lines go indefinitely from top to bottom or from bottom up. Definitions and Formula Horizontal lines have the following characteristics: They have Zero Slope. They are drawn from left to right through the y-axis. The equation only has one constant to determine where it will be drawn. Such as (y = 5, y = - 3, y = 17, etc.) And the points of such equations have the same value for the 'y' on the given points such as {(-2, 4), (9, 4)}, {(3, -7), (-4, -7), (8, -7)} Vertical lines have the following characteristics: They have an Undefined Slope. They are drawn from top to bottom through the x-axis. The equation only has one constant to determine where it will be drawn. Such as (x = 1, y = 4, y = -11, etc.) And the points of such equations have the same value for the 'x' on the given points such as {(6, -1), (6, 7)}, {(1, 2), (1, -6), (1, 17), (1, 0)} Atlantic Union Conference Teacher Bulletin Page 3 of 20
4 Key Concepts The following are some of the graphs we have seen and their equations. A. If the line going from left to right is rising, then we say the slope is a Positive Slope. Equations: B. If the Line is horizontal, then the slope is Zero. Equation: y = b (b is the y-intercept and a constant) The equation for this graph would be: y = 6 Atlantic Union Conference Teacher Bulletin Page 4 of 20
5 C. If the line going from left to right is falling, then we say the slope is Negative. Equations: D. If the line is a vertical line, then the slope is Undefined. Equation: x = b (b is the x-intercept and a constant) The equation for this graph would be: x = -3 Atlantic Union Conference Teacher Bulletin Page 5 of 20
6 Let s write equations for the given points and also learn how to graph them. 1. Write an equation for a horizontal line and graph. Remember: Horizontal lines have Zero Slope. Why? When the Slope formula is used to find the slope to two points which lie in a horizontal position from each other, the result will be which equals zero. (# represents any number) Therefore we say that horizontal lines have Zero Slope. A. Write an equation of the line which passes through (6, 3), (-5, 3). i. Points (6, 3), (-5, 3) ii. m = 0 iii. y = 3 B. Write an equation of the line which passes through (1, -4), (7, -4). i. Points (1, -4), (7, -4) ii. m = 0 iii. y = -4 Atlantic Union Conference Teacher Bulletin Page 6 of 20
7 C. Write an equation of the line which passes through (0, 4), (10, 4). i. Points (0, 4), (10, 4) ii. m = 0 iii. y = 4 2. Write an equation for a Vertical Line and graph. Remember: Vertical Lines have an Undefined Slope. Why? When the Slope formula is used to find the slope to two points which lie in vertical position to each other, the result will be. Because nothing can be divided by zero. We say the line has an Undefined Slope. (#represents any number) Therefore we say that vertical lines have an Undefined Slope. For example: because But? What number multiplied by zero produces the answer of six? There isn't one. Hence, vertical lines have Undefined Slopes. A. Write an equation of the line which passes through (3, 6), (3, -5). i. Points (3, 6), ( 3, -5) ii. m = Undefined iii. x = 3 Atlantic Union Conference Teacher Bulletin Page 7 of 20
8 B. Write an equation of the line which passes through (-4, 1), (-4, 7). i. Points (-4, 1), ( -4, 7) ii. m = Undefined iii. x = -4 C. Write an equation of the line which passes through (4, 0), (4, 10). i. Points (4, 0), ( 4, 10) ii. m = Undefined iii. x = 4 Atlantic Union Conference Teacher Bulletin Page 8 of 20
9 Equations for Horizontal and Vertical Lines ~ Student Practice Worksheet Name Date Grade If not given, state whether the line has a slope of Zero or Undefined. Also, state whether it is a Horizontal or a Vertical Line. Graph the line. 1. (7, 8), (1, 8) 3. (6, 2), m = 0 2. (4, -1.5), (4, 4.5) 4. (-2, -3), undefined Atlantic Union Conference Teacher Bulletin Page 9 of 20
10 5. (6, 4), (3, 4) 7. (-5, 6), (-5, -9) 6. (-2, -5), slope = 0 8. (-4, 5), (4, 5) Atlantic Union Conference Teacher Bulletin Page 10 of 20
11 9. (2, 5), m = undefined 10. (2, 5), m = 0 Atlantic Union Conference Teacher Bulletin Page 11 of 20
12 The Mathematics in Lines: Equations for Horizontal and Vertical Lines Equations for Horizontal and Vertical Lines ~ Student Practice Worksheet Answer Key Name Date Grade If not given, state whether the line has a slope of Zero or Undefined. Also, state whether it is a Horizontal or a Vertical Line. Graph the line. 1. (7, 8), (1, 8) 3. (6, 2), m = 0 Slope = 0, Horizontal Line Horizontal Line 2. (4, -1.5), (4, 4.5) Slope = undefined, Vertical Line 4. (-2, -3), undefined Vertical Line Atlantic Union Conference Teacher Bulletin Page 12 of 20
13 The Mathematics in Lines: Equations for Horizontal and Vertical Lines 5. (6, 4), (3, 4) Slope = Zero, Horizontal Line 7. (-5, 6), (-5, -9) Slope = Undefined, Horizontal Line 6. (-2, -5), slope = 0 Horizontal Line 8. (-4, 5), (4, 5) Slope = Zero, Horizontal Line Atlantic Union Conference Teacher Bulletin Page 13 of 20
14 The Mathematics in Lines: Equations for Horizontal and Vertical Lines 9. (2, 5), m = undefined Vertical Line 10. (2, 5), m = 0 Horizontal Line Atlantic Union Conference Teacher Bulletin Page 14 of 20
15 The Mathematics in Lines: Equations for Horizontal and Vertical Lines Equations for Horizontal and Vertical Lines ~ Student Practice Worksheet Rubric Mechanics Criteria No major math Major math errors errors or serious or serious flaws flaws in reasoning. in reasoning. No math errors May be some serious math error or flaws in reasoning. Blank answers Quiz Grading Rubric: Problem Total points of Correct Answer Problem Total points of Correct Answer Atlantic Union Conference Teacher Bulletin Page 15 of 20
16 The Mathematics in Lines: Equations for Horizontal and Vertical Lines Equations for Horizontal and Vertical Lines ~ Quiz Name Date Grade If not given, state whether the line has a slope of Zero or Undefined. Also, state whether it is a Horizontal or a Vertical Line. Graph the line. 1. (3, -1), (3, -4) 3. (5, -3), Slope = Zero 2. (5, 8), (-2, 8) 4. (-6, -6), Undefined Atlantic Union Conference Teacher Bulletin Page 16 of 20
17 The Mathematics in Lines: Equations for Horizontal and Vertical Lines 5. (2, -6), (2, 5) Atlantic Union Conference Teacher Bulletin Page 17 of 20
18 The Mathematics in Lines: Equations for Horizontal and Vertical Lines Equations for Horizontal and Vertical Lines ~ Quiz Answer Key Name Date Grade If not given, state whether the line has a slope of Zero or Undefined. Also, state whether it is a Horizontal or a Vertical Line. Graph the line. 1. (3, -1), (3, -4) Slope = Undefined, Vertical Line 3. (5, -3), Slope = Zero Horizontal Line 2. (5, 5), (-2, 5) Slope = Zero, Horizontal Line 4. (-6, -6), Undefined Vertical Line Atlantic Union Conference Teacher Bulletin Page 18 of 20
19 The Mathematics in Lines: Equations for Horizontal and Vertical Lines 5. (2, -6), (2, 5) Slope = Undefined, Vertical Line Atlantic Union Conference Teacher Bulletin Page 19 of 20
20 The Mathematics in Lines: Equations for Horizontal and Vertical Lines Equations for Horizontal and Vertical Lines ~ Quiz Rubric Mechanics Criteria No major math Major math errors errors or serious or serious flaws flaws in reasoning. in reasoning. No math errors May be some serious math error or flaws in reasoning. Blank answers Quiz Grading Rubric: Problem Total points of Correct Answer Problem Total points of Correct Answer Atlantic Union Conference Teacher Bulletin Page 20 of 20
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