1. Slope & Rate of Change

2. What is slope? The slope of a nonvertical line is the ratio of the vertical change (the rise) to the horizontal change (the run) between any two points on the line. The slope of a nonvertical line is the ratio of the vertical change (the rise) to the horizontal change (the run) between any two points on the line.

3. We commonly use the letter m for slope. We can find the slope of any two points (x1, y1) and (x2, y2) on a line by using the formula: We commonly use the letter m for slope. We can find the slope of any two points (x1, y1) and (x2, y2) on a line by using the formula:

4. Four Types of Slope 1. positive, m > 0; line rises from left to right

5. 2. negative, m < 0; line falls from left to right

6. 3. zero, m = 0 (horizontal lines); imagine that you can walk on it

7. 4. undefined, some # divided by zero (vertical lines); imagine trying to walk up a wall

8. Find the slope of the line between the given points. (2,2) and (8,9) (2,2) and (8,9) (-2,3) and (2,1) (-2,3) and (2,1)

9. Find the slope between the given points. (3, 2) and (-1, 2) (3, 2) and (-1, 2) (4, -6) and (4, 0) (4, -6) and (4, 0)

10. Guided Practice p. 23 # 1, 2 and p. 24 #3, 4

11. Rate of Change A rate of change compares a change in one quantity to a change in another quantity, i.e. slope. The only thing that is different is that we include units. A rate of change compares a change in one quantity to a change in another quantity, i.e. slope. The only thing that is different is that we include units. There are two variables, the independent variable and the dependent variable. There are two variables, the independent variable and the dependent variable. The dependent variable “depends” on the independent variable. The dependent variable “depends” on the independent variable.

12. Example: The table shows the amount of water evaporating from a swimming pool on a hot day. Find the rate of change in gallons with respect to time. Time (hours) 2612 Gallons evaporated 4.513.527

13. Solution: Change in gals. = 13.5 – 4.5 = 9 gal. Change in gals. = 13.5 – 4.5 = 9 gal. Change in time 6 – 2 4 hrs. Change in time 6 – 2 4 hrs. Now, since rate of change is per hour, we need to divide, so 9/4 becomes 2.25 and the rate of change is 2.25 gallons per hour 2.25 gallons per hour

14. Assignment: Pg. 25, #’s 1-27 Pg. 25, #’s 1-27 Be sure to show your graphs when needed and show your work when doing the slope formula. Be sure to show your graphs when needed and show your work when doing the slope formula.