Question

A driver starts a journey with $25$ gallons in the tank of his car. The car burns $5$ gallons for every $100$ miles. Assuming that the amount of gasoline in the tank decreases linearly,
(a) Write a linear function that relates the number of gallons $G$ left in the tank after a journey of $x$ miles
(b) What is the value and meaning of the slope of the graph of $G$?
(c) What is the value and meaning of the $x$ intercept?

Answer 1

Let x represents miles and G represents gallons then

At $x=0$ 0 miles the tank has $25$ gallons $G=25$

At $x=100$ 100 miles the tank has $5$ gallons $G=5$

Hence linear Equation becomes

$G\left(x\right)-25=\frac{25-5}{0-100}\left(x\right)$

$G\left(x\right)-25=\frac{-20}{100}\left(x\right)$

$G\left(x\right)=\frac{-1}{5}\left(x\right)+25$

$G\left(x\right)=\frac{-1}{5}x+25$

$\left(b\right)$

The slope of graph G is $-\frac{1}{5}$

It means on every journey of 1 miles the gallon is decreasing by $\frac{1}{5}$

$\left(c\right)$

The x intercept can be find when $G=0$ SO putting $G=0$ in equation

$G\left(x\right)=\frac{-1}{5}x+25$ we get

$x=125$ it means the car can travel $125miles$ in 25 gallons