Question

time (hours) distance (miles) 2 90 3 135 5 225 6 270 what is the constant of proportionality (in miles per hour) based on the table? 90 135 45 2

Explanation:

Step1: Recall the formula for constant of proportionality

The constant of proportionality \( k \) in a proportional relationship \( y = kx \) (where \( y \) is distance and \( x \) is time) is given by \( k=\frac{y}{x} \).

Step2: Calculate using the first pair of values

Using the first row: \( x = 2 \) hours, \( y = 90 \) miles. So \( k=\frac{90}{2}=45 \).

Step3: Verify with other values (optional but good practice)

Using the second row: \( x = 3 \), \( y = 135 \). \( k=\frac{135}{3}=45 \).
Using the third row: \( x = 5 \), \( y = 225 \). \( k=\frac{225}{5}=45 \).
Using the fourth row: \( x = 6 \), \( y = 270 \). \( k=\frac{270}{6}=45 \).

All calculations give the same value, so the constant of proportionality is 45.

Answer:

45