Question

this graph shows how the amount of gas remaining is related to the number of miles driven.
gas left in alices tank
if alices tank ended up with 3 gallons of gas, how far must alice have driven?
\boxed{} miles

Explanation:

Step1: Determine the slope of the line

The line goes from (0, 10) to (100, 0). The slope \( m \) is calculated as \( \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 10}{100 - 0} = -\frac{1}{10} \). The equation of the line is \( y = -\frac{1}{10}x + 10 \), where \( y \) is gas remaining (gallons) and \( x \) is miles driven.

Step2: Substitute \( y = 3 \) into the equation

We have \( 3 = -\frac{1}{10}x + 10 \). Subtract 10 from both sides: \( 3 - 10 = -\frac{1}{10}x \), so \( -7 = -\frac{1}{10}x \). Multiply both sides by -10: \( x = 70 \).

Answer:

70