Jackson wanted to drive a car that uses less gasoline, so he bought a hybrid.

Question

This table shows the relationship between the volume of gasoline Jackson's car uses when driving on the highway (in gallons), x, and the distance he drives it on the highway (in miles), y.
x (gallons) y (miles)
0.5 24
3 144
14.5 696
18.5 888
According to the values in the table, do x and y have a proportional relationship?
yes
no

Answer 1

To determine if \( x \) (gallons of gasoline) and \( y \) (miles driven) have a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) is constant for all pairs of values in the table.

Calculating the ratios for each pair:

1. For \( x = 0.5 \) and \( y = 24 \): \[ \frac{y}{x} = \frac{24}{0.5} = 48 \]

2. For \( x = 3 \) and \( y = 144 \): \[ \frac{y}{x} = \frac{144}{3} = 48 \]

3. For \( x = 14.5 \) and \( y = 696 \): \[ \frac{y}{x} = \frac{696}{14.5} = 48 \]

4. For \( x = 18.5 \) and \( y = 888 \): \[ \frac{y}{x} = \frac{888}{18.5} = 48 \]

Since the ratio \( \frac{y}{x} \) is constant (equal to 48) for all values, we can conclude that \( x \) and \( y \) do have a proportional relationship.

The answer is yes.