1. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 1

2. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 2 Graphs of Linear Equations and Inequalities; Functions Chapter 3

3. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 3 3.3 Slope of a Line

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 4 3.3 Slope of a Line Objectives 1.Find the slope of a line given two points. 2.Find the slope from the equation of a line. 3.Use slope to determine whether two lines are parallel, perpendicular, or neither. 4.Solve problems involving average rate of change.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 5 Find the Slope of a Line Given Two Points 3.3 Slope of a Line An important characteristic of a line is its slant or steepness, as viewed from left to right. We measure steepness by comparing the vertical change to the horizontal change while moving along the line. This steepness measure is called the slope of the line.

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 6 3.3 Slope of a Line Begin at point Q and move to point P. The vertical change, the rise, is the change in y-values. The horizontal change, the run, is the change in x-values. (continued) Find the Slope of a Line Given Two Points

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 7 3.3 Slope of a Line The slope is the ratio of the vertical change in y (the rise) to the horizontal change in x (the run). Find the Slope of a Line Given Two Points

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 8 3.3 Slope of a Line Example 1 Find the slope of the line in the figure. Find the Slope of a Line Given Two Points

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 9 3.3 Slope of a Line Find the Slope of a Line Given Two Points

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 10 3.3 Slope of a Line The concept of slope is used in many everyday situations (see Section 3.3 applied exercises). Find the Slope of a Line Given Two Points

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 11 3.3 Slope of a Line General Equation for Slope Find the Slope of a Line Given Two Points

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 12 3.3 Slope of a Line Find the Slope of a Line Given Two Points

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 13 3.3 Slope of a Line Example 2a Find the slope of the line through (–4, 7) and (1, –2). Find the Slope of a Line Given Two Points (continued)

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 14 3.3 Slope of a Line Example 2a Find the slope of the line through (–4, 7) and (1, –2). Find the Slope of a Line Given Two Points

15. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 15 3.3 Slope of a Line Find the Slope of a Line Given Two Points

16. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 16 3.3 Slope of a Line Example 3 Find the slope of the line through (–8, 4) and (2, 4). Find the Slope of a Line Given Two Points All horizontal lines have slope 0.

17. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 17 3.3 Slope of a Line Example 4 Find the slope of the line through (6, 2) and (6,  4). Find the Slope of a Line Given Two Points All vertical lines have undefined slope.

18. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 18 3.3 Slope of a Line Find the Slope of a Line Given Two Points

19. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 19 3.3 Slope of a Line Find the Slope from the Equation of a Line

20. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 20 3.3 Slope of a Line Example 5a Find the slope of the line 2x – 5y = 4. Find the Slope of a Line Given Two Points

21. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 21 3.3 Slope of a Line Use slope to determine whether two lines are parallel, perpendicular, or neither.

22. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 22 3.3 Slope of a Line Example 6a Decide whether the lines are parallel, perpendicular, or neither. Use slope to determine whether two lines are parallel, perpendicular, or neither. Find the slope of each line by solving each equation for y. (continued)

23. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 23 3.3 Slope of a Line Example 6a Decide whether the lines are parallel, perpendicular, or neither. Use slope to determine whether two lines are parallel, perpendicular, or neither. The slopes are negative reciprocals. The lines are perpendicular.

24. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 24 3.3 Slope of a Line Example 6b, d Decide whether the lines are parallel, perpendicular, or neither. Use slope to determine whether two lines are parallel, perpendicular, or neither. The lines are not parallel, nor are they perpendicular.

25. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 25 3.3 Slope of a Line Solve problems using average rate of change. We know that the slope of a line is the ratio of the vertical change in y to the corresponding horizontal change in x. Thus, the slope formula applied to any two points on the line gives the average rate of change in y per unit change in x, where the value of y depends on the value of x.

26. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 26 3.3 Slope of a Line Example 7 The graph approximates the average number of hours per year spent watching cable and satellite TV for each person in the United States during the years 2000 through 2005. Find the average rate of change in number of hours per year. Solve problems using average rate of change.

27. Copyright © 2010 Pearson Education, Inc. All rights reserved. 3.3 – Slide 27 3.3 Slope of a Line Example 7 The graph approximates the average number of hours per year spent watching cable and satellite TV for each person in the United States during the years 2000 through 2005. Find the average rate of change in number of hours per year. Solve problems using average rate of change. This means that the average time per person spent watching cable and satellite TV increased by 58 hr per year from 2000 through 2005.