Question

Given the table for x, lawns mowed and y, money earned:

x - # of lawns 7 6 2 9 3
y - $ earned 294 252 84 378 126

Answer 1

To analyze the relationship between the number of lawns mowed (x) and the money earned (y), we can find the cost (or money earned per lawn mowed) by calculating the ratio of y to x for each pair of values. Here's how to do that:

1. Calculate the earnings per lawn for each data point:

- For \( x = 7 \), \( y = 294 \):
\[
\text{Earnings per lawn} = \frac{294}{7} = 42
\]

- For \( x = 6 \), \( y = 252 \):
\[
\text{Earnings per lawn} = \frac{252}{6} = 42
\]

- For \( x = 2 \), \( y = 84 \):
\[
\text{Earnings per lawn} = \frac{84}{2} = 42
\]

- For \( x = 9 \), \( y = 378 \):
\[
\text{Earnings per lawn} = \frac{378}{9} = 42
\]

- For \( x = 3 \), \( y = 126 \):
\[
\text{Earnings per lawn} = \frac{126}{3} = 42
\]

2. Summarizing the findings:
- In each case, the earnings per lawn mowed is consistently \( \$42 \).

This indicates a linear relationship, where the earnings can be expressed with the equation:
\[
y = 42x
\]

Where:
- \( y \) is the money earned,
- \( x \) is the number of lawns mowed, and
- The $42 represents the constant earning per lawn mowed.

Feel free to ask if you would like to perform any further analysis or calculations!