1. Warm-Up
The table shows the horizontal and vertical distance from the base of the mountains at several poles along the path of a ski lift. The poles are connected by cables. Between which two poles is the cables' path the steepest? How do you know?

2. 02/09/17
3.2 Rate of Change
Essential Question: Why is a constant rate of change the key characteristic of a  linear function?

3. What is rate of Change?
Rate of change shows the relationship between two changing quantities. When one quantity depends on the other the following is true.

4. Finding rate of Change
The table shows the distance a band marches over time. Is the rate of change in distance with respect to time constant? What does the rate of change represent?

5. Finding Rate of change
Do you get the same rate of change if you use nonconsecutive rows of the table?
What is the rate of change between rows 1 and 3?
What is the rate of change between rows 2 and 4?
What is the rate of change between rows 1 and 4?

6. Is it Constant?
Determine if the rate of change is constant.

7. Is it Constant?
Determine if the rate of change is constant.

8. What is Rate of change??
A ratio of the difference in the dependent variable to the difference in the independent variable.

9. Slope & Rate of Change Solving Real-Life Problems Using Slope
Slope Formula:
Determine independent and dependent variables
Time is always an independent variable (x-values)
Find two points and use slope formula to determine rate of change!

10. Rate of Change Given points
Find the slope of the line formed by the points (2,5) and (1,3).

11. Rate of Change Given points
Find the slope of the line formed by the points (4,2) and (4,-3). Find the slope of the line formed by the points (-1,-3) and (5,-3).

12. Rate of Change
A climber is on a hike. After 2 hours, he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 70 feet. What is the average rate of change?

13. Rate of Change
The table shows the year and population of a city. Find the rate of change.

14. Rate of Change
A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water and 100 feet below the surface after 40 seconds. What is the scuba divers rate of change?