1. Finding rates of change from tables and graphs.
WHAT YOU’LL LEARN:
Finding rates of change from tables and graphs.
AND WHY:
To find rates of change in real-world situations, such as the rate of descent for a parachute or the cost of renting a computer.

2. Suppose you type 140 words in 4 minutes. What is your typing rate?
RATES OF CHANGE
Suppose you type 140 words in 4 minutes. What is your typing rate?
140 words
4 min
35 words
1 min =
The number of words depends on the number of minutes you type. So, the number of words is the dependent variable.

3. RATES OF CHANGE $19.99 $3.99 5 yd 1 yd = 268.8 mi 22.4 mi 12 gal 1 gal
Write each as a rate.
You buy 5 yards of fabric for $19.95.
You travel mi on 12 gal of gasoline.
$19.99
5 yd
$3.99
1 yd =
268.8 mi
12 gal
22.4 mi
1 gal =

4. change in the dependent variable change in the independent variable =
RATES OF CHANGE
You use a rate of change to find the amount of one quantity per one unit of another, such as typing 35 words in 1 min.
The RATE OF CHANGE allows you to see the relationship between two quantities that are changing.
rate of change
change in the dependent variable
change in the independent variable =

5. dependent variable (RISE) independent variable (RUN)
RATES OF CHANGE
On a graph, you show the dependent variable on the vertical axis and the independent variable on the horizontal axis.
change in the
dependent variable (RISE)
independent variable (RUN)

6. Rate of Change of a Linear Relationship
rise
run
Rate of Change =
The rate of change of a linear relationship is the steepness of the line.
When a graph shows a straight line (with a constant rate of change), it represents a linear relationship

7. LINEAR FUNCTIONS 2 The rate of change is . 3 8 6 4 2
Is this relationship linear? Why?
Find the Rate of Change:
Graph x y 8 6 4 2
2 units
3 units
The rate of change is 2 3

8. LINEAR FUNCTIONS
From a table, you must find the difference in the dependent variables (y) and compare that to the difference in the independent variables (x).
Table
Change in y values
Change in x values
x y
0 1
3 3
6 5
9 7 3 2 3 2 3 2
2 units
3 units
When tables show a constant rate of change, they represent a linear relationship

9. LINEAR FUNCTIONS Is this relationship linear? Why?
Find the Rate of Change:

10. Find the rate of change for each situation.
LINEAR FUNCTIONS
Find the rate of change:
Does this represent a linear function? Why?
Price of Oregano
Cost (dollars)
Weight (ounces) 2 1 1 6
$1 buys 6 oz of oregano.

11. About 1 gal used for every 15 mi.
LINEAR FUNCTIONS
Find the rate of change:
Does this represent a linear function? Why?
A Tank of Gas 15 10 5
Fuel in Tank (gallons)
Miles Traveled 1 15
About 1 gal used for every 15 mi.

12. Find the rate of change for each situation.
LINEAR FUNCTIONS
Find the rate of change:
Does this represent a linear function? Why?
x y 1 -2 -5 -8 1 -3
YES 1 -3 1 -3

13. Find the rate of change for each situation.
LINEAR FUNCTIONS
Find the rate of change:
Does this represent a linear function? Why?
x y 1 4
8 9 2 1 NO 2 3 2 5

14. Find the rate of change for each situation.
LINEAR FUNCTIONS
Find the rate of change:
Does this represent a linear function? Why?
x y
0 3 6 9 12 1 3
YES 1 3 1 3

15. Find the rate of change for each situation.
LINEAR FUNCTIONS
Find the rate of change:
Does this represent a linear function? Why?
x y
1 3
3 7
4 9
7 15 2 4
YES 1 2 3 6
Rate of change is 2.