1. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 1 Section 3.3 Slope Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1

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3. 3 Slope The change in the y values is the vertical change or the “Rise”. The change in the x values is the horizontal change or the “Run.” m is commonly used to denote the slope of a line. The slope of a line is related to its steepness. When the slope is positive, the line rises from left to right. When the slope is negative, the line falls from left to right.

4. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 4 x1x1 x2x2 y1y1 y2y2 Run x 2 – x 1 Rise y 2 -y 1 Visual Representation of Slope

5. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 5 Slope of a Line The slope of the line through the two distinct points and is m, where Note that you may call either point However, don’t subtract in one order in the numerator and use another order for subtraction in the denominator - or the sign of your slope will be wrong.

6. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 6 Slopes of LinesEXAMPLE SOLUTION Find the slope of the line passing through the pair of points. Then explain what the slope means. Remember, the slope is obtained as follows: This means that for every six units that the line (that passes through both points) travels up, it also travels 11 units to the right.

7. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 7 Slopes of Lines Possibilities for a Line’s Slope Positive SlopeNegative Slope Zero SlopeUndefined Slope

8. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 8 8 Objective #1: Example

9. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 9 9 Objective #1: Example

10. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 10 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 10 Objective #1: Example

11. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 11 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 11 Objective #1: Example

12. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 12 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 12 Objective #1: Example

13. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 13 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 13 Objective #1: Example

14. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 14 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 14

15. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 15 Parallel Lines Slope and Parallel Lines 1) If two non-vertical lines are parallel, then they have the same slope. 2) If two distinct non-vertical lines have the same slope, then they are parallel. 3) Two distinct vertical lines, each with undefined slope, are parallel.

16. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 16 Parallel Lines

17. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 17 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 17 Objective #2: Example

18. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 18 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 18 Objective #2: Example

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20. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 20 Perpendicular Lines Slope and Perpendicular Lines 3) A horizontal line having zero slope is perpendicular to a vertical line having undefined slope.

21. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 21 Perpendicular Lines

22. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 22 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 22 Objective #3: Example

23. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 23 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 23 Objective #3: Example

24. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 24 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 24 Objective #3: Example

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26. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 26 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 26

27. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 27 Slope as Rate of Change Slope is defined as the ratio of a change in y to a corresponding change in x. It tells how fast y is changing with respect to x. Thus, the slope of a line represents its rate of change.

28. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 28 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 28 Objective #4: Example

29. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 29 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 29 Objective #4: Example

30. Copyright © 2013, 2009, 2006 Pearson Education, Inc. 30 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 30 Objective #4: Example