Question

before leaving for a road trip to mount rushmore, myras dad stops to get gas for his van. the total cost of the gas increases as myras dad fills the van. this situation can be modeled as a linear relationship.

Explanation:

Step1: Identify two points

From the graph, when \( x = 8 \) (gallons), \( y=\$30 \); when \( x = 16 \), \( y = \$60 \).

Step2: Calculate slope

Slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{60 - 30}{16 - 8}=\frac{30}{8}=\frac{15}{4} = 3.75 \).

Step3: Determine equation

Using point - slope form \( y - y_1=m(x - x_1) \), with \( (x_1,y_1)=(0,0) \) (since it passes through origin), the equation is \( y = 3.75x \), meaning cost per gallon is \(\$3.75\).

Answer:

The cost per gallon of gas is \(\$3.75\) (or the linear equation is \( y = 3.75x \) where \( x \) is gallons and \( y \) is total cost).