Question

A car starts a journey with a full tank of gas. The equation y=16 - 0.05x relates the number of gallons of gas, y, left in the tank to the number of miles the car has traveled, x. A. What are the x- and y-intercepts of the graph of this equation? B. What does x-intercept represent in the context of this problem? C. What does y-intercept represent in the context of this problem?

Answer 1

We are given that a car starts a journey with a full tank of gas. The equation
`y=16-0.05x` relates the number of gallons of gas (y) left in the tank to the number of miles the car has traveled(x).

A. We will find y intercept by substituting x=0 in our equation,

`y=16-0.05*0`

`y=16`

Now let us find our x-intercept by substituting y=0 in our equation,

`0=16-0.05x`

`0.05x=16`

`x=(16)/(0.05)=320`

Therefore, x-intercept is 320 and y-intercept is 16.

B. Our x-intercept represents that after travelling 320 miles there were 0 or none gallons of gas left in tank.

C. Our y-intercept represents that there were 16 gallons of gas in car tank when car started the journey.