The table below shows that the number of miles driven by Rajani is directly proportional to the number of gallons she used.

Question

Gallons UsedGallons Used Miles DrivenMiles Driven
3838 1162, point, 81162.8
4444 1346, point, 41346.4
4848 1468, point, 81468.8
What is the constant of proportionality between the number of miles driven and the number of gallons used?

Answer 1

To find the constant of proportionality between the number of miles driven and the number of gallons used, you can use the formula:

\[ k = \frac{\text{Miles Driven}}{\text{Gallons Used}} \]

Let's calculate the constant of proportionality \( k \) using the given data:

1. For \( 38 \) gallons used and \( 1162.8 \) miles driven: \[ k = \frac{1162.8}{38} \approx 30.7 \]

2. For \( 44 \) gallons used and \( 1346.4 \) miles driven: \[ k = \frac{1346.4}{44} \approx 30.7 \]

3. For \( 48 \) gallons used and \( 1468.8 \) miles driven: \[ k = \frac{1468.8}{48} \approx 30.7 \]

In each case, the constant of proportionality \( k \) is approximately \( 30.7 \).

Thus, the constant of proportionality between the number of miles driven and the number of gallons used is approximately \( 30.7 \).