Question

1. determine the constant of proportionality. express your answer as y = kx

lawns mowed (x) | 9 | 2 | 8 | 7 | 3
dollars earned (y) | 387 | 86 | 344 | 301 | 129
for every lawn mowed ______ dollars were earned.

Explanation:

Step1: Recall the formula for proportionality

The relationship \( y = kx \) means \( k=\frac{y}{x} \). We can calculate \( k \) for each pair of \( x \) and \( y \) to check consistency.

Step2: Calculate \( k \) for the first pair

For \( x = 9 \) and \( y = 387 \), \( k=\frac{387}{9}=43 \).

Step3: Calculate \( k \) for the second pair

For \( x = 2 \) and \( y = 86 \), \( k=\frac{86}{2}=43 \).

Step4: Calculate \( k \) for the third pair

For \( x = 8 \) and \( y = 344 \), \( k=\frac{344}{8}=43 \).

Step5: Calculate \( k \) for the fourth pair

For \( x = 7 \) and \( y = 301 \), \( k=\frac{301}{7}=43 \).

Step6: Calculate \( k \) for the fifth pair

For \( x = 3 \) and \( y = 129 \), \( k=\frac{129}{3}=43 \).

Answer:

43