1. Rate of Change

2. Learning Goals I can calculate and interpret the rate of change from a graph and a table of values I can identify the units of rate of change given the units of the two variables

3. Rate of change What does the “rate of change” mean in the context of this situation? How could we find it? What other names do we have for the “rate of change”?

4. How to calculate Rate of Change, AKA Slope Select the two points between which you want to know the rate of change. It’s helpful to label one point as (x 1, y 1 ) and the other as (x 2, y 2 ) Complete the formula for slope: y 2 -y 1 x 2 -x 1 This formula means: change from one y to another change from one x to another

5. Rate of Change Ex. 1 Calculate the rate of change What does the rate of change mean here? Time (min) Height of airplane (m) 02000 41400

6. Comparing Rate of Change Ex. 2 The distance required to stop a car depends on the speed at which the car is travelling These tables show the reaction distance and braking distance needed to stop a car on dry pavement for given speeds REACTION Distance: the distance the car travels from the time the driver decides to stop the car until he/she applies the brakes BRAKING Distance: the distance the car travels from the time the brakes are applied until the car actually stops.

7. Comparing Rates of Change Ex. 2 SPEED (km/h) REACTION Distance (m) 00 102 204 306 408 5010 Change in distance Change in speed Description of the Rate of Change:

8. SPEED (km/h) BRAKING Distance (m) 00.0 100.5 202.0 304.5 408.0 5012.5 Change in distance Change in speed Description of the Rate of Change: Comparing Rates of Change Ex. 2

9. Graph it! Describe how the graph reflects the rates of change across the data

10. Example 2

11. Identifying Rates of Change in a Table & Graph This table shows the change in height of a tomato plant from germination until the tomatoes ripen. TIME (weeks) 024681012141618 HEIGHT (cm) 0510204058758690 Determine when the rate of change in the height is: i) Zeroii) Constantiii) Changing

12. This table shows the change in height of a tomato plants from germination until the tomatoes ripen. TIME (weeks) 024681012141618 HEIGHT (cm) 0510204058758690 Determine when the rate of change in the height is: i) Zeroii) Constantiii) Changing STEP 1: Find the first differences STEP 2: Graph the data

13. Consolidate Rates of Change GIVEN A TABLE OR GRAPH, WE CAN IDENTIFY WHEN THE RATE OF CHANGE IS ZERO, CONSTANT, OR CHANGING WITHOUT ACTUALLY CALCULATING THE RATES OF CHANGE In a table, we look at the first differences In a graph, we decide whether the points lie on a line Identifying Rates of Change in a Table or Graph RATE OF CHANGE TABLEEx. of GRAPH Zero Constant Changing

14. Learning Goals I can calculate and interpret the rate of change from a graph and a table of values I can identify the units of rate of change given the units of the two variables Homework: Pg. 284 # 2-4, 7, 11