Question

Arianna filled up her car with gas before embarking on a road trip across the country. Let G represent the number of gallons of gas remaining in her gas tank after driving for t hours. A graph of G is shown below. Write an equation for G then state the x- intercept of the graph and determine its interpretation in the context of the problem.

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

G = gallons remaining in the tank

t = hours

equation = ?

x- intercept of the graph = ?

Step 02:

We must analyze the graph to find the solution.

point 1 ( 0 , 15) x1 = 0 y1 = 15

point 2 (12 , 0) x2 = 12 y2 = 0

slope formula

`m\text{ = }\frac{y2\text{ -y1}}{x2-x1}=(0-15)/(12-0)=(-15)/(12)=-1.25`

slope-intercept form of the line

y = mx + b

m = -1.25

b = y-intercept = 15

G = -1.25x + 15

x- intercept of the graph = 12

After 12 hours there is no gas left in the tank.

The answer is:

G = -1.25x + 15

x- intercept of the graph = 12

After 12 hours there is no gas left in the tank.