1. Reminder We do not have class this Thursday (September 25). I will not be in my office during my regular office hours tomorrow (Sept 24).

2. Copyright © Houghton Mifflin Company. All rights reserved.3 | 2 In the picture, the third step of the ladder is 3 feet above the ground. 3 ft 1 ft It is also a horizontal distance of 1 foot from the base of the ladder. The ladder meets the ceiling at a horizontal distance of 4½ feet from the base of the ladder, ? ft How high is the ceiling? 4½ ft

3. Copyright © Houghton Mifflin Company. All rights reserved.3 | 3 3 ft 1 ft4½ ft ? ft How high is the ceiling? 13.5

4. Copyright © Houghton Mifflin Company. All rights reserved.3 | 4 A fundamental property of lines is that the ratio of “rise” to “run” is the same no matter what two points on the line are used. rise run rise run rise run = rise run

5. Copyright © Houghton Mifflin Company. All rights reserved.3 | 5 SLOPE

6. Copyright © Houghton Mifflin Company. All rights reserved.3 | 6 x y 1 2 3 4 5 6 7 8 9 8765432187654321 The slope of this line is m = = 2. rise run Slope is the ratio of rise to run between any two points. Slope is a comparison of rise (vertical change) to run (horizontal change) between points. Slope = = The letter m is usually used for slope. yxyx

7. Copyright © Houghton Mifflin Company. All rights reserved.3 | 7 x y 1 2 3 4 5 6 7 8 9 8765432187654321 5 10 Here is the same line. What if we compute the slope using 2 other points on the line? Slope =

8. Copyright © Houghton Mifflin Company. All rights reserved.3 | 8 x y 1 2 3 4 5 6 7 8 9 8765432187654321 Slope is a measure of steepness of a line. If slope (m) is – the line is falling left to right. The function is decreasing. If slope (m) = 0, the line is horizontal. For a vertical line, slope is not defined. If slope (m) is + the line is rising left to right. The function is increasing. m = +2 m = –1 m = 0

9. Copyright © Houghton Mifflin Company. All rights reserved.3 | 9 What is the slope of our ladder? 3 ft 1 ft 3

10. Copyright © Houghton Mifflin Company. All rights reserved.3 | 10 The slope of a line is the average rate of change of its height. In other words, the slope of a line tells us the change in height (y) for each one unit change along the horizontal (x). x y 1 2 3 4 5 6 7 8 9 8765432187654321

11. Copyright © Houghton Mifflin Company. All rights reserved.3 | 11 x y 1 2 3 4 5 6 7 8 9 8765432187654321 5 10 (1, 5) (–4, –5) Slope =

12. Copyright © Houghton Mifflin Company. All rights reserved.3 | 12 x y 1 2 3 4 5 6 7 8 9 8765432187654321 What is the slope of the line shown? (2,2) (0,-1) =

13. Copyright © Houghton Mifflin Company. All rights reserved.3 | 13 x y 1 2 3 4 5 6 7 8 9 8765432187654321 What is the slope of the line shown? (0,2) (4,-3) == vertical intercept horizontal intercept

14. Copyright © Houghton Mifflin Company. All rights reserved.3 | 14 Computing slope: Example 1: Find the slope of the line that passes through the points (5, 7) and (-3, 1). Example 2:Find the slope of the line with horizontal intercept 5 and vertical intercept 2. Example 3:Find the slope of the line that passes through the points (4, 5) and (9, 5). Example 4:Find the slope of the line that passes through the points (-3, 2) and (-3, 9).

15. Copyright © Houghton Mifflin Company. All rights reserved.3 | 15 Computing slope: Example 1: Find the slope of the line that passes through the points (5, 7) and (-3, 1). Example 2:Find the slope of the line with horizontal intercept 5 and vertical intercept 2. Example 3:Find the slope of the line that passes through the points (4, 5) and (9, 5). Example 4:Find the slope of the line that passes through the points (-3, 2) and (-3, 9). ¾

16. Copyright © Houghton Mifflin Company. All rights reserved.3 | 16 Computing slope: Example 1: Find the slope of the line that passes through the points (5, 7) and (-3, 1). Example 2:Find the slope of the line with horizontal intercept 5 and vertical intercept 2. Example 3:Find the slope of the line that passes through the points (4, 5) and (9, 5). Example 4:Find the slope of the line that passes through the points (-3, 2) and (-3, 9). ¾ –2..5

17. Copyright © Houghton Mifflin Company. All rights reserved.3 | 17 Computing slope: Example 1: Find the slope of the line that passes through the points (5, 7) and (-3, 1). Example 2:Find the slope of the line with horizontal intercept 5 and vertical intercept 2. Example 3:Find the slope of the line that passes through the points (4, 5) and (9, 5). Example 4:Find the slope of the line that passes through the points (-3, 2) and (-3, 9). ¾ 0 (the line is horizontal) –2..5

18. Copyright © Houghton Mifflin Company. All rights reserved.3 | 18 Computing slope: Example 1: Find the slope of the line that passes through the points (5, 7) and (-3, 1). Example 2:Find the slope of the line with horizontal intercept 5 and vertical intercept 2. Example 3:Find the slope of the line that passes through the points (4, 5) and (9, 5). Example 4:Find the slope of the line that passes through the points (-3, 2) and (-3, 9). ¾ 0 (the line is horizontal) No Slope (the line is vertical) –2..5

19. Copyright © Houghton Mifflin Company. All rights reserved.3 | 19 x y 1 2 3 4 5 6 7 8 9 8765432187654321 On coordinate axes, draw a line whose slope is 2 and which has vertical intercept –7.  What is the horizontal intercept?

20. Copyright © Houghton Mifflin Company. All rights reserved.3 | 20 x y 1 2 3 4 5 6 7 8 9 8765432187654321 On coordinate axes, draw a line whose slope is –½ and which has horizontal intercept 3. 

21. Copyright © Houghton Mifflin Company. All rights reserved.3 | 21 24 ft Questions: 1.What is the slope of the roof? 2. What is the horizontal intercept of the roof? ? 12 ft 15 ft Suppose we draw in an x and y-axis. ● 5 ft 3.If we move 5 feet to the right of center, how high is the roof?

22. Copyright © Houghton Mifflin Company. All rights reserved.3 | 22 Homework: Read Section 3.1 ( through middle of page 214) Page 221 # S-1, S-2, S-3, S-5, S-7, S-8 Pages 222 – 224 # 1 – 5, 7, 13