To analyze the relationship between the number of lawns mowed (x) and the money earned (y), we can address each part of your question as follows:
a. Every lawn mowed is \(_\) dollars earned.
To find the earnings per lawn, we can calculate the unit rate by dividing the amount earned (y) by the number of lawns mowed (x) for each entry.
- For 7 lawns: \( \frac{294}{7} = 42 \)
- For 6 lawns: \( \frac{252}{6} = 42 \)
- For 2 lawns: \( \frac{84}{2} = 42 \)
- For 9 lawns: \( \frac{378}{9} = 42 \)
- For 3 lawns: \( \frac{126}{3} = 42 \)
From above, we see that every lawn mowed earns 42 dollars.
Completed statement: Every lawn mowed is 42 dollars earned.
b. Dollars/1 lawn mowed is called a \(_\).
The amount earned per lawn mowed is termed a unit rate.
Completed statement: Dollars/1 lawn mowed is called a unit rate.
c. This relationship is \(_\) because \(_\).
To determine if the relationship is proportional or non-proportional, we look at the ratios. In this case, since the earnings per lawn mowed (42 dollars) are constant, this indicates a linear relationship. Since the relationship is linear and the ratio of y to x is constant, the relationship is also proportional.
Completed statement: This relationship is proportional because the earnings per lawn mowed remains constant at 42 dollars (which means a consistent ratio exists between x and y).
Final Completion
- a. Every lawn mowed is 42 dollars earned.
- b. Dollars/1 lawn mowed is called a unit rate.
- c. This relationship is proportional because the earnings per lawn are constant at 42 dollars.
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