1. Constant Rate of Change
Linear Equations & Slope

2. A linear relationship has a constant rate of change.
Robert can download two songs from the Internet each minute. This is shown in the table and in the graph.
Number of Songs 2 4 6 8
Time (minutes) 1 3
Pick several pairs of points and find the rate of change between them. What is true of the rates?
Relationships that have straight-line graphs, like this one, are called linear relationships. As the time in minutes increases by 1, the number of songs increases by 2.
A linear relationship has a constant rate of change.
Number of Songs
Time (minutes)

3. Is the relationship between day and balance linear?No

4. Is the relationship between month and temperature a constant rate of change?No

5. Is the relationship between cost and minutes a constant rate of change?
Yes

6. Find the constant rate of change, if possible.
Number of Transactions
Balance ($) 3
170 6
140 9
110 12 80
The balance is an account after several transactions is shown. Is the relationship between the balance and number of transactions linear?
Find the constant rate of change, if possible.
The constant rate of change is -30/3 or $10 per transaction. This means that each transaction involved a $10 withdrawal.
As the number of transactions increases by 3, the balance in the account decreases by $30.

7. Determine whether the relationship between the two quantities described in each table is linear. If so, find the constant rate of change. If not, explain your reasoning.

8. Cost ($)
Number of items
Each item is $0.33 or 3 for $1.

9. Identify Proportion Relationships
Constant Rate of Change
Degrees Celsius 9 18 27 36
Degrees Fahrenheit 32 37 42 47 52
To determine if the two scales are proportional, express the relationship between the degrees for several columns as a ratio.
Since the ratios are not the same, the relationship between degrees Fahrenheit degrees Celsius are not proportional.

10. Constant Rate of Change
Linear Equations & Slope