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
(4 points)
a. Every lawn mowed is
dollars earned.
b. Dollars/1 lawn mowed is called a
c. This relationship is !
because
tickets sold is SO earned
:: 0
:: proportional
:: non proportional
5
:: non linear
:: unit rate
:: variable
:: 84
Decreasing
:: 42
x - # of lawns
7
6
2
9
3
y - $ earned
294
252
84
378
126
(4 points)
a. Every lawn mowed is
dollars earned.
b. Dollars/1 lawn mowed is called a
c. This relationship is !
because
tickets sold is SO earned
:: 0
:: proportional
:: non proportional
5
:: non linear
:: unit rate
:: variable
:: 84
Decreasing
:: 42
Answers
GPT-4o mini
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.
### 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.