1. 8-3: Slope Objectives The student will be able to: find the slope of a line given 2 points and a graph. First by rise/run then using the formula! Find slope from tables.

2. What does the sign mean? Where would you see this sign?

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

4. Picking out type of slope. Flashcards PDF slides for examples. Using the whiteboards, I am going to show you 14 slides. You are to write the type of slope. +, -, 0 (horizontal), or undefined (vertical)!

5. Let’s Review Draw the 4 types of slope: 1. 2.3.4. Slope is the STEEPNESS of a LINE!

6. Slope can be expressed 4 different ways: 1. A line has a positive slope if it is going uphill from left to right. 2. A line has a negative slope if it is going downhill from left to right.

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

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

9. Warm-UP Everyone needs 2 colored pencils. For the NCTM activity worksheet “Just Slope”. Please following along.

10. Rise/Run Pay attention to the next few examples.

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

12. 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!

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

14. Remember… Slope can be: Positive Negative 0/# = 0 #/0 = Undefined Fractions, improper, 9/7, 11/9, 15/2, etc. Decimals ½ = 0.5, ¼ = 0.25, etc.

15. Let’s try more Using the colored pencils and the NCTM activity triangle worksheet, we will complete more rise/run problems.NCTM activity triangle worksheet We will do some together then you will complete some on your own.

16. Who uses this stuff? Let’s think of several jobs that uses angles/slope/rate of change? (look at pdf)look at pdf 1. roofer

17. Recall 1. Horizontal Lines have _________ slope. 2. Vertical Lines have ________ slope. 3. Draw the 4 types of slope AND label the slope A. B. C. D. m = m = zero undefined

18. Synonyms for slope? 1. angle

19. Slope, do we need a formula? You may not always be given a graph of the line to determine slope using rise/run. So we need another method. Using the slope formula, you can ALWAYS find slope if you know 2 points. Remember slope is a rate of change. Change in y’s/ change in x’s

20. 1) 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! STEPS for using this formula: 1.LABEL your points- EVERYTIME!!!!!!!! 2.Plug in the formula and simplify the fraction.

21. 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?

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

23. Graphic Organizer Let’s use a graphic organizer to guide us for the method of finding slope using the formula. Remember HORIZONTAL lines = VERTICAL lines = zero slope Undefined slope

24. 4) Find the slope of the line that passes through (3, 5) and (-1, 4). Label the points: A. 4 B. -4 C. ¼ D. - ¼

25. 5) Determine the slope of the line shown. A. -2Could do this 2 ways!! B. -½ C. ½ D. 2 What would be a real world ex? Think of a pool…

26. Practice, Whiteboards 1. LABEL 2. plug in 3. simplify 1. (1, 1), (3, 4) 2. (0, 0), (5, 4) 3. (-2, 2), (-1, -2) 4. (7, -4), (9, -1) 5. (3, 5), (-2, 5) 6. (-1, 3), (-1, 0)

27. Review Handout with slope as a formula (partner slope activity). In partners of 2- here are the groups  Please complete, check with a neighbor and turn in.

28. Collinear Points Lie on the same line. Points are collinear if they have the same slope.

29. Let’s Find Out Are (3, 5), (4, 7) (7, 13) collinear? Calculate the slope the first two points: (3, 5) and (4, 7). Calculate the slope for the second pair of points (4, 7) and (7, 13). Yes.

30. You Try… Are (8, 9), (5, 3), and (2, -2) collinear? No.

31. 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

32. 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

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

34. 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)