Question

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

boxes of candy (x) | 3 | 9 | 7 | 10 | 2
pieces of candy (y) | 60 | 180 | 140 | 200 | 40
for every box of candy you get ______ pieces.

Explanation:

Step1: Recall the formula for proportionality

The formula for direct proportionality is \( y = kx \), where \( k \) is the constant of proportionality. To find \( k \), we can use the formula \( k=\frac{y}{x} \) for each pair of \( x \) and \( y \) values and check if it's constant.

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

For \( x = 3 \) and \( y = 60 \), we calculate \( k=\frac{y}{x}=\frac{60}{3}=20 \).

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

For \( x = 9 \) and \( y = 180 \), we calculate \( k=\frac{y}{x}=\frac{180}{9}=20 \).

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

For \( x = 7 \) and \( y = 140 \), we calculate \( k=\frac{y}{x}=\frac{140}{7}=20 \).

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

For \( x = 10 \) and \( y = 200 \), we calculate \( k=\frac{y}{x}=\frac{200}{10}=20 \).

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

For \( x = 2 \) and \( y = 40 \), we calculate \( k=\frac{y}{x}=\frac{40}{2}=20 \).

Answer:

20