Question
Charlie wants to go to a concert with his friends. To earn enough money for a concert ticket, Charlie is mowing lawns for his neighbors. He charges the same rate for each neighbor. There is a linear relationship between the number of lawns Charlie mows and the amount he has left to earn. 2 4 6 8 10 12 14 16 18 20 $20 $40 $60 $80 $100 $120 $140 $160 $180 $200 x y Number of lawns Amount left to earn ($) Describe the rate of change for this relationship. The amount Charlie has left to earn increases decreases by $1.50 $10.00 $15.00 $30.00 $60.00 $150.00 per lawn. Submit
Answers
GPT-4o mini
To analyze the rate of change in the relationship between the number of lawns Charlie mows (x) and the amount he has left to earn (y), we can look at the given data points:
- When Charlie mows 2 lawns, he has $20 left to earn.
- When he mows 4 lawns, he has $40 left to earn.
- This pattern continues up to 20 lawns, where he has $200 left to earn.
From these points, we can calculate the rate of change (slope) of the linear relationship:
- The amount left to earn increases by $20 for every 2 lawns mowed.
To find the rate of change per lawn, we can use the slope formula:
\[
\text{Rate of Change} = \frac{\text{Change in y}}{\text{Change in x}} = \frac{20 - 0}{2 - 0} = \frac{20}{2} = 10
\]
Thus, the amount Charlie has left to earn **decreases by $10.00 per lawn** he mows. This means for each lawn he mows, the amount he has left to earn goes down by $10.00.
So the correct description of the rate of change for this relationship is:
**The amount Charlie has left to earn decreases by $10.00 per lawn.**
- When Charlie mows 2 lawns, he has $20 left to earn.
- When he mows 4 lawns, he has $40 left to earn.
- This pattern continues up to 20 lawns, where he has $200 left to earn.
From these points, we can calculate the rate of change (slope) of the linear relationship:
- The amount left to earn increases by $20 for every 2 lawns mowed.
To find the rate of change per lawn, we can use the slope formula:
\[
\text{Rate of Change} = \frac{\text{Change in y}}{\text{Change in x}} = \frac{20 - 0}{2 - 0} = \frac{20}{2} = 10
\]
Thus, the amount Charlie has left to earn **decreases by $10.00 per lawn** he mows. This means for each lawn he mows, the amount he has left to earn goes down by $10.00.
So the correct description of the rate of change for this relationship is:
**The amount Charlie has left to earn decreases by $10.00 per lawn.**