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3. 4-1 Understanding Slope

4. Video Tutor Help Slope: graph the line Word problem: rate of change Finding a unit rateFinding a unit rate (Chapter 4) Comparing unit ratesComparing unit rates (Chapter 4) Finding slope using rise/runFinding slope using rise/run (4-1) Understanding Slope Finding the slope of a line Finding Slope From a Table Slope-intercept form Khan Academy 4-1 Understanding Slope Course 3 Slope "Slope" is a fundamental concept in mathematics. Slope is often defined as "the rise over the run"... but why?

5. Video Tutor Help Finding slope using rise/run

6. Worksheets 4-1 Note-Taking Guide 4-1Practice 4-1 Guided Problem Solving

7. Vocabulary Practice Chapter 4 Vocabulary (Electronic) Flash Cards

8. Additional Lesson Examples 4-1 Step-by-Step Examples

9. Lesson Readiness 4-1 Problem of the Day 4-1 Lesson Quiz

13. Slope You can find the slope of a line by using the coordinates of any two points on the line. One point can be represented by (x 1, y 1 ) and the other by (x 2, y 2 ). The small numbers slightly below x and y are called subscripts.

14. Slope Formula The slope m of a line passing through points (x 1, y 1 ) and (x 2, y 2 ) is the ratio of the difference in the y-coordinates to the corresponding difference in the x-coordinates. Where x 2 ≠ x 1 (x 1, y 1 ) (x 2, y 2 ) m = y 2 – y 1 x 2 – x 1

15. Study Tip It does not matter which point you define as and. However, the coordinates of both points must be used in the same order. (x 1, y 1 ) (x 2, y 2 )

17. Example 4-1a Find the slope of the line that passes through A(3, 3) and B(2, 0). Simplify. Definition of slope Positive Slope

18. Example 4-1b Check When going from left to right, the graph of the line slants upward. This is consistent with a positive slope. Answer: The slope is 3.

19. Example 4-2a Find the slope of the line that passes through X(–2, 3) and Y(3, 0). Definition of slope Simplify. Negative Slope

20. Example 4-2b Check When going from left to right, the graph of the line slants downward. This is consistent with a negative slope. Answer: The slope is.

21. Example 4-3a Find the slope of the line that passes through P(6, 5) and Q(2, 5). Definition of slope Simplify. Zero Slope

22. Example 4-3b Answer: The slope is 0. The slope of any horizontal line is 0.

23. Example 4-4a Find the slope of the line that passes through G(2, 4) and H(2, 6). Definition of slope Simplify. Undefined Slope

24. Example 4-4b Answer: Division by 0 is not defined. So, the slope is undefined. The slope of any vertical line is undefined.

25. Example 4-1a Find the slope of a hill that rises 30 feet for every horizontal change of 150 feet. Definition of slope rise = 30 feet, run = 150 feet Simplify. Answer: The slope of the hill isor 0.2. Use Rise and Run to Find Slope

26. Example 4-1b Find the slope of a hill that rises 40 feet for every horizontal change of 100 feet. Answer:

27. Example 4-2a Find the slope of the line. Definition of slope Answer: The slope is 3. Positive Slope

28. Example 4-2b Find the slope of the line. Answer:

29. Example 4-3a Find the slope of the line. Answer: The slope is. Definition of slope Negative Slope

30. Example 4-3b Find the slope of the line. Answer:

31. Example 4-4a Find the slope of the line. Answer: The slope is 0. Definition of slope Zero Slope

32. Example 4-4b Find the slope of the line. Answer: 0

33. Example 4-5a Find the slope of the line. Answer: The slope is undefined. Division by 0 is undefined. So, the slope is undefined. Undefined Slope

34. Example 4-5b Find the slope of the line. Answer: undefined

35. Understanding Slope LESSON 4-1 Using coordinates, find the slope of the line between P (–2, 3) and Q (–1, –1). 3 – (–1) –2 – (–1) = Subtract the coordinates of point Q from the coordinates of point P. slope = change in y change in x Simplify. = or –4 4– 14– 1 Additional Examples

37. Understanding Slope LESSON 4-1 Find the slope of each line. State whether the slope is zero or undefined. a. line k Division by zero is undefined. The slope of a vertical line is undefined. b. line p The slope of a horizontal line is zero. slope = = = 0 2 – 2 –2 – 3 0 –5 slope = = 1 – (–3) 2 – 2 4040 Additional Examples

39. Understanding Slope Graph the distance-cost data below. Connect the points with a line. Then find the rate of change. LESSON 4-1 Distance (mi)0100200 300 400 500 Cost ($)025 50 75 100 125 The amount spent on fuel increases $1 for every 4 miles driven. rate of Change Use coordinates of two points. change in y change in x = slope 25 – 0 100 – 0 == Subtract and simplify. 25 100 = 1414 = Additional Examples