Question

Avery filled up her car with gas before embarking on a road trip across the country. Let GG represent the number of gallons of gas remaining in her gas tank after driving for tt hours.The table below has select values showing the linear relationship between tt and G.G. Determine the number of gallons of gas used per hour driven.

Answer 1

Since the table is showing a linear relationship, we can model the problem as follows:

$G(t)=mt+b$

Where:

b = y-intercept (Initial amount of gas)

m = Slope ( Gallons of gas used per hour)

so:

Using the data provided by the table:

$\begin{gathered} t=0.5;G(0.5)=9 \\ 9=0.5m+b_{\text{ }}(1) \\ ---------- \\ t=4;G(4)=2 \\ 2=4m+b_{\text{ }}(2) \end{gathered}$

Using elimination method:

$\begin{gathered} (2)-(1) \\ 2-9=4m-0.5m+b-b \\ -7=3.5m \\ m=-\frac{7}{3.5} \\ m=-2 \end{gathered}$

Therefore, the number of gallons of gas used per hour driven is 2.