Question

Keith is driving on the highway. He begins the trip with 16 gallons of gas in his car. The car uses up one gallon of gas every 20 miles.Let G represent the number of gallons of gas he has left in his tank, and let D represent the total distance (in miles) he has traveled. Write an equation relating G to D, and then graph your equation using the axes below.

Answer 1

An equation relating G to D is:

`G=(-D)/(20)+16`

The graph of the equation is:

Step-by-step explanation

Note: The general formula for a linear equation is y = mx + c

Now, using the model of a linear equation, we have:

`G=Dm+c`

'c' is the y-intercept of the equation, (i.e the initial value of G, when D = 0).

So if Keith starts the trip with 16 gallons of gas in his car, we have c = 16.

'm' is the slope of the line, (i.e an increase of 1 in the value of D causes an increase of 'm' in the value of G).

So if the car uses one gallon every 20 miles, the value of m is -1/20 (an increase of 20 in D causes a decrease of 1 in G).

Hence, an equation relating G to D is:

`G=(-D)/(20)+16`

The graph of the equation using a graphing tool is: