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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
=

Respuesta :

calculista

Answer:

Part a) The rate is equal to [tex]-\frac{7}{2}\frac{gallons}{hour}[/tex]

Part b) [tex]y=-3.5x+17[/tex]

Step-by-step explanation:

step 1

Let

x-----> the number of hours

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

we know that

For [tex]x=0, y=17\ gallons[/tex] -----> represent the y-intercept

For [tex]x=4\ hours, y=3\ gallons[/tex]

Find the rate (slope of the linear equation)

[tex]m=\frac{3-17}{4-0}[/tex]

[tex]m=-\frac{14}{4}[/tex]

simplify

[tex]m=-\frac{7}{2}\frac{gallons}{hours}[/tex]

step 2

Find the equation of the line

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

[tex]y=mx+b[/tex]

we have

[tex]m=-\frac{7}{2}=-3.5[/tex]

[tex]b=17[/tex]

substitute

[tex]y=-3.5x+17[/tex]

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