Chapter 3 Graphing Linear Equations Section 2 Graphing

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Chapter 3 Graphing Linear Equations Section 2 Graphing Linear Equations and Their Intercepts Copyright

Chapter 3 Graphing Linear Equations Section 2 Graphing Linear Equations and Their Intercepts Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 1

Concept Intercepts A point at which a graph crosses the x-axis is called an

Concept Intercepts A point at which a graph crosses the x-axis is called an x-intercept and a point at which a graph crosses the y-axis is called a yintercept. To find an x-intercept, substitute 0 for y and solve for x. To find a y-intercept, substitute 0 for x and solve for y. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 2

Example 1 Find the coordinates of any x-intercepts and y-intercepts. The graph crosses the

Example 1 Find the coordinates of any x-intercepts and y-intercepts. The graph crosses the x-axis at the point (4, 0). This is the x-intercept (4, 0) y-intercept (0, 2) The y-intercept is (0, 2). Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 3

Example 2 Intercepts Find the intercepts: x-intercept y-intercept Copyright © 2016, 2012, and 2009

Example 2 Intercepts Find the intercepts: x-intercept y-intercept Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 4

Concept Graphing a Linear Equation Using Its Intercepts Find the x-intercept and the y-intercept,

Concept Graphing a Linear Equation Using Its Intercepts Find the x-intercept and the y-intercept, and plot them on the plane. A third point, with an arbitrarily chosen value of x, can be used as a check point. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 5

Example 3 Graphing a Linear Equation Using Its Intercepts Graph: x-intercept y-intercept Copyright ©

Example 3 Graphing a Linear Equation Using Its Intercepts Graph: x-intercept y-intercept Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 6

Example Graph 3 x – 4 y = 0. Find the x-intercept and two

Example Graph 3 x – 4 y = 0. Find the x-intercept and two other points. Choose x = 0. Choose x = 4. 4 The x-intercept is at the origin (0, 0). This point is also the y-intercept. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 7

Example 4 Table of Solutions x- and yintercept: x y 0 0 4 3

Example 4 Table of Solutions x- and yintercept: x y 0 0 4 3 4 3 Plot the solutions and connect the points to form the line. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 8

Concept Graphing Horizontal Lines To graph the line plot the yintercept on the y-axis

Concept Graphing Horizontal Lines To graph the line plot the yintercept on the y-axis and draw a horizontal line through this point. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 9

Example 5 Graphing Horizontal Lines Graph: Copyright © 2016, 2012, and 2009 Pearson Education,

Example 5 Graphing Horizontal Lines Graph: Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 10

Concept Graphing Vertical Lines To graph the line plot the xintercept on the x-axis

Concept Graphing Vertical Lines To graph the line plot the xintercept on the x-axis and draw a vertical line through this point. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 11

Example Graphing Horizontal Lines 6 Graph: Copyright © 2016, 2012, and 2009 Pearson Education,

Example Graphing Horizontal Lines 6 Graph: Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 12

Example Kenneth borrowed $4200 from his parents for a car, promising to pay them

Example Kenneth borrowed $4200 from his parents for a car, promising to pay them $75 per month until he had paid off the loan. The amount of money (y) that Kenneth owes his parents after x months have passed is given by the equation y = 4200 – 75 x. Use the graph of this equation (on the next slide) to answer the following questions (since the number of months cannot be negative, the graph begins at x = 0): Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 13

Example a. What does the y-intercept represent in this situation? The y-intercept is at

Example a. What does the y-intercept represent in this situation? The y-intercept is at (0, 4200). It tells us that after borrowing the money from his parents, Kenneth owes them $4200. b. What does the x-intercept represent in this situation? The x-intercepts is at (56, 0). It tells us that Kenneth will pay off his debt in 56 months. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 14