Cody wants to go to a concert with his friends. To earn enough money for a concert ticket, Cody is mowing lawns for his neighbors. He charges the same rate for each neighbor.

Question

There is a linear relationship between the number of lawns Cody mows and the amount he has left to earn.
Number of lawns Amount left to earn
2 $120.00
4 $90.00
6 $60.00
Describe the rate of change for this relationship.
The amount Cody has left to earn
by
per lawn.

Answer 1

To find the rate of change for the relationship between the number of lawns Cody mows and the amount he has left to earn, we can calculate the change in the amount left to earn (in dollars) for each additional lawn mowed.

Let's look at the values provided:

• For 2 lawns, the amount left to earn is $120.
• For 4 lawns, the amount left to earn is $90.
• For 6 lawns, the amount left to earn is $60.

Now, let's calculate the change in the amount left to earn for the changes in the number of lawns mowed.

1. From 2 lawns to 4 lawns:

   • Change in lawns = 4 - 2 = 2 lawns
   • Change in amount left to earn = $90 - $120 = -$30

   The rate of change for this interval is: \[ \text{Rate of Change} = \frac{\text{Change in Amount}}{\text{Change in Lawns}} = \frac{-30}{2} = -15 \text{ dollars per lawn} \]

2. From 4 lawns to 6 lawns:

   • Change in lawns = 6 - 4 = 2 lawns
   • Change in amount left to earn = $60 - $90 = -$30

   The rate of change for this interval is the same: \[ \text{Rate of Change} = \frac{-30}{2} = -15 \text{ dollars per lawn} \]

Since the rate of change is consistent in both intervals, we conclude that the relationship is linear.

Thus, the rate of change for this relationship is: The amount Cody has left to earn decreases by $15 per lawn mowed.