2. 4.5 Finding The Slope of a Line

3. What is the meaning of this sign? 1.Icy Road Ahead 2.Steep Road Ahead 3.Curvy Road Ahead 4.Trucks Entering Highway Ahead

4. Slopes are commonly associated with mountains.

5. The slope we are studying is associated with the graph of a line.

6. Definitions of Slope The tilt or inclination of a line The ratio of vertical change to horizontal change. The change in y over the change in x Δy Δx

7. Tilt or Inclination FROM LEFT TO RIGHT!!!! POSITIVE SLOPE NEGATIVE SLOPE SLOPE IS ZERO SLOPE IS UNDEFINED y = # x = #

8. Tell me slope of each line POSITIVE NEGATIVE ZERO POSITIVE

9. Slope can be expressed different ways: A line has a positive slope if it is going uphill from left to right. A line has a negative slope if it is going downhill from left to right. UP or DOWN RIGHT

10. Graph (3,2) and (-1,-1)

11. Draw a line through the points.

12. Rise 3 4 Run THE SLOPE IS 3 4

13. Find the slope of the following line. The slope is… 1 2

14. Find the slope of the line. The slope is…. -3

15. When given the graph, it is easier to apply “rise over run”. 1) Determine the slope of the line.

16. Determine the slope of the line shown. 1.-2 2.-½ 3.½ 4.2

17. Determine the slope of the line. The line is decreasing (slope is negative). -2 1 Find points on the graph. Use two of them and apply rise over run.

18. What is the slope of a horizontal line? The line doesn’t rise! All horizontal lines have a slope of 0.

19. What is the slope of a vertical line? The line doesn’t run! All vertical lines have an undefined slope.

20. Find the slope of these lines. Black line 3 Red Line 1 Blue Line-1/2

21. Find the slope of these lines Orange line = 0 Green Line = Undefined

22. Determining Slope Rise=1 Slope= 1212 Slope=3 Rise=6 Run =2 Rise=12 Run =4

23. Let’s find the slope of a line with two points, WITHOUT LOOKING AT A GRAPH. REMEMBER THE SLOPE FORMULA???!!!!!

24. Determining Slope without graphing (-4, -6) (2, 5) Pick 2 points on the line Find the change in the Y- coordinates by subtracting(rise) Find the change in the X- coordinates by subtracting(run) 5-(-6) 2-(-4) = 11 6

25. 2) Find the slope of the line that passes through the points (-2, -2) and (4, 1). When given points, it is easier to use the formula! y 2 is the y coordinate of the 2 nd ordered pair (y 2 = 1) y 1 is the y coordinate of the 1 st ordered pair (y 1 = -2)

26. 3) Find the slope of the line that goes through the points (-5, 3) and (2, 1). x 1 y 1 x 2 y 2

27. Sample Problems: Find the slope of the line thru the points given:  (-3,-1) and (-2,4)  (-3,4) and (2,-2) x 1 y 1 x 2 y 2 x 1 y 1 x 2 y 2

28. Independent Practice: Calculate the slope for each pair of points. Classify each slope as positive, negative, zero, or undefined. 1. (2, 2) and (3, 5)2. (0, 0) and (3, 0) 3. (-2, -1) and (-1, -4)4. (2, 3) and (2, 7) 5. (-1, -1) and (5, 5)6. (8, 4) and (6, 4) Slope: 3 Classification: Positive Slope: -3 Classification: Negative Slope: 1 Classification: Positive Slope: 0 Classification: Zero Slope: Undefined Classification: Vertical Slope: 0 Classification: Horizontal

29. EVERYONE GET A COMMUNICATOR!!!

30. 1 Draw a line through the point (2,0) that has a slope of 3. 1. Graph the ordered pair (2, 0). 2. From (2, 0), apply rise over run (write 3 as a fraction). 3. Plot a point at this location. 4. Draw a straight line through the points. 3

31. If you know the slope and one point on the line you can draw the line. Example: slope is 1/3 and the point (-2,-1)

32. Now you draw a line. Given: slope is 2/3 and the point is (1,0) Given: slope is –3 and the point is (–2,4) Given: slope is 1 and the point is (2,3)

33. Graph the line y = 3x +1, then tell me the slope of that line after you graphed it. The slope is 3 x y -2 0 1 2 -5 -2 1 4 7

34. Graph the line 2x + y = 4, then tell me the slope of that line after you graphed it. x y -2 0 1 2 8642086420 The slope is -2y = -2x + 4

35. Graph the line y = -5, then tell me the slope of that line after you graphed it. x y -2 0 1 2 -5 The slope is 0

36. Graph the line y = 2x, then tell me the slope of that line after you graphed it. x y -2 0 1 2 -4 -2 0 2 4 The slope is 2

37. Graph the line y = 3x - 2, then tell me the slope of that line after you graphed it. x y -2 0 1 2 -8 -5 -2 1 4 The slope is 3

38. Graph the line 2x + 3y = 6, then tell me the slope of that line after you graphed it. x y -6 -3 0 3 6 4 2 0 -2 The slope is - 2/3

39. Graph the line y = -x - 2, then tell me the slope of that line after you graphed it. x y -2 0 1 2 0 -2 -3 -4 The slope is -1

40. Graph the line 3x – 4y = 12, then tell me the slope of that line after you graphed it. x y -8 -4 0 4 8 -9 -6 -3 0 3 The slope is 3/4

41. Graph the line x – y = 5, then tell me the slope of that line after you graphed it. x y -2 0 1 2 -7 -6 -5 -4 -3 The slope is 1y = x - 5

42. The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r. To solve this, plug the given information into the formula

43. To solve for r, simplify and write as a proportion. Cross multiply. 1(-4) = 4(4 – r)

44. Simplify and solve the equation. 1(-4) = 4(4 – r) -4 = 16 – 4r -16 -20 = -4r -4 5 = r The ordered pairs are (5, 6) and (4, 2)