1. Finding The Slope of a Line

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

3. What does the 7% mean? 7% is the slope of the road. It means the road drops 7 feet vertically for every 100 feet horizontally. 7% So, what is slope??? Slope is the steepness of a line. 7 feet 100 feet Just copy this definition

4. 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. Copy this slide

5. Finding the slope of a line on a graph

6. Graph (3, 2) and (-1, -1) Just watch

7. Draw a line through the points. Just watch

8. Now that we have our line lets find its slope. Remember we are finding the following ratio: Vertical orRise Horizontal Run Just read

9. VERTICAL Change or the RISE 3 Just watch

10. HORIZONTAL Change or the RUN 4 3 Just watch

11. Vertical Rise Horizontal Run 3 4 Just watch

12. When given the graph, it is easier to apply “rise over run”. Determine the slope of the line. Just watch

13. Start with the lower point and count how much you rise and run to get to the other point! Determine the slope of the line. 6 3 run 3 6 == rise Notice the slope is positive AND the line increases! Just watch

14. Determine the slope of the line shown. 1.-2 2.-½ 3.½ 4.2 If there are no points on the graph place points on the line at an intersection. Just watch

15. Determine the slope of the line shown. 1.-2 2.-½ 3.½ 4.2 If there are no points on the graph place points on the line at an intersection. 2 Rise Run 2 Just watch

16. Find the slope of these lines

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

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

19. Remember the word “VUXHOY” Vertical lines Undefined slope X = number; This is the equation of the line. Horizontal lines O - zero is the slope Y = number; This is the equation of the line. Copy in notebook

20.  Record notes in foldable first under the GRAPH heading.  Partner Work – Pass out worksheet. Find the slopes of the graphs.  Go ahead on slides for finding slopes other ways.

21. Finding the slope of a line when given two points

22. 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! Label your points. y1y1 y2y2 x1x1 x2x2 m represents slope Take Notes!

23. Did you notice that Example #1 and Example #2 were the same problem written differently? (-2, -2) and (4, 1) 6 3 You can do the problems either way! Which one do you think is easiest? Just watch

24. 3) Find the slope of the line that goes through the points (-5, 3) and (2, 1). y2y2 y1y1 x2x2 x1x1 Write formula Label points Substitute number for variables. Take Notes!

25. Find the slope of the line that passes through (2, 5) and (3, 6). 1.2 2.1 3.- 1 4.-2 1 st – Write Formula for finding slope 2 nd – Label your points 3 rd – Substitute numbers in for variables. 4 th – Simplify. Do in notebook!

26. Find the slope of the line that passes through (4, 1) and (-4, 1). 1.0 2.8 3.- 8 4.-1/8 Do in Notebook!

27. Find the slope of the line that passes through (4, 1) and (-6, -4). 1.2 2.-2 3.-1/2 4.1/2 Do in Notebook!

28. Find the slope of the line that passes through (-2, 4) and (10, 0). 1.1/3 2.-1/3 3.-1/2 4.1/2 Do in Notebook!

29. Find the slope of the line that passes through (3, 2) and (3, -2). 1.0 2.4 3.-4 4.undefined Do in Notebook!

30. Find the slope of the line that passes through (2, 7) and (-2, -3). 1.5/2 2.-5/2 3.-4 4.0 Do in Notebook!

31.  Record notes in foldable first under Ordered Pairs heading.  Activity– Pass out worksheet. Find the slopes of the graphs.  Go ahead on slides for finding slopes other ways.

32. Finding the slope of a line from a table

33. Calculate slope from a table. XY 110 220 330 440 550

34. Is this function linear? Calculate slope from a table. XY 322 1036 1750 2464 3178

35. Finding the slope from word problems

36. Slope from Word Problems The pitch of a roof is the number of feet the roof rises for each 12 feet horizontally. If a roof has a pitch of 8, what is the slope expressed as a positive number?

37. Slope from Word Problems A daily newspaper had 12,125 subscribers when it began publication. Five years later it had 10,100 subscribers. What is the average yearly rate of change in the number of subscribers for the five year period?

38. Drawing a line when given one point and the slope

39. 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

40. 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)

41. 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)

42. Finding a missing coordinate.

43. 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

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

45. 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)