Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall

Chapter 3 Graphs and Functions

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall 3.4 The Slope of a Line

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall

Find the slope of the line containing the points (4, −3) and (2, 2). Graph the line. Solution If we let (x 1, y 1 ) be (4, −3) and (x 2, y 2 ) be (2, 2), then Example 2 continued

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Note: If we let (x 1, y 1 ) be (2, 2) and (x 2, y 2 ) be (4, −3), then we get the same result. (2,2) (4,−3) Notice this is an example of a negative slope. The graph of the line moves downward, or decreases, as we go from left to right.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Slope-Intercept Form When a linear equation in two variables is written in slope-intercept form, y = mx + b Then m is the slope of the line and (0, b) is the y-intercept of the line. slope y-intercept

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Find the slope and y-intercept of the line –3x + y = −5. Solution Write the equation in slope-intercept form--solve for y. –3x + y = −5 Once we have the equation in the form of y = mx + b, we can read the slope and y-intercept. slope is 3 y-intercept is (0, – 5) Example 4 y = 3x + 5 –3x + 3x + y = −5 + 3x

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Find the slope and y-intercept of the line 2x – 6y = 12. Solution Solve the linear equation for y. – 6y = – 2x + 12 Subtract 2x from both sides. y = x – 2 Divide both sides by –6. The equation is now in the form of y = mx + b. slope is y-intercept is (0, – 2) Example 4

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall The slope of any vertical line is undefined. The slope of any horizontal line is 0.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Find the slope of the line x = −7. Solution Example 6 To find the slope, we find two ordered pair solutions of x = −7. The solutions must have an x-value of −7. We will use (−7, 0) and (−7, 4). continued

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall The slope of a vertical line is undefined. continued x = −7

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Find the slope of the line y = −4. Solution Example 7 To find the slope, we find two ordered pair solutions of y = −4. The solutions must have an y-value of −4. We will use (0,−4) and (6, −4). continued

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall The slope of the horizontal line is zero. continued y = −4

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall

Determine whether the following lines are parallel, perpendicular, or neither. –5x + y = –6 x + 5y = 5 Solution Solve both equations for y. Equation 1Equation 2 –5x + y = –6 x + 5y = 5 y = 5x – 6 The first equation has a slope of 5 and the second equation has a slope of, the lines are perpendicular. Example 8