Question

Suppose you start with a full tank of gas (17 gallons) in your truck. After driving 4 hours, you now have 3 gallons left.

If x is the number of hours you have been driving, then y is the number of gallons left in the tank.

At what rate is your truck using gas? State your answer as a reduced fraction.


Incorrect gallons per hour

Find an equation of a line in the form y = mx + b that describes the amount of gas in your tank.

y
=

Answer 1

Part a) The rate is equal to
`-(7)/(2)(gallons)/(hour)`

Part b)
`y=-3.5x+17`

Explanation:

step 1

Let

x-----> the number of hours

y----> the number of gallons left in the tank

we know that

For
`x=0, y=17\ gallons` -----> represent the y-intercept

For
`x=4\ hours, y=3\ gallons`

Find the rate (slope of the linear equation)

`m=(3-17)/(4-0)`

`m=-(14)/(4)`

simplify

`m=-(7)/(2)(gallons)/(hours)`

step 2

Find the equation of the line

the equation of the line in slope intercept form is equal to

`y=mx+b`

we have

`m=-(7)/(2)=-3.5`

`b=17`

substitute

`y=-3.5x+17`