Question

!!20 POINTS!! Claire 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 slope of the graph and determine its interpretation in the context of the problem.

Answer 1

Answer:

$G=-\frac{5}{4}t+15$

Slope = $-\frac{5}{4}$

Step-by-step explanation:

Let the equation representing the number of gallons left in the gas tank is,

G = mt + b

Where m = slope of the line

b = y-intercept of the line

Slope of the line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is,

'm' = $\frac{y_2-y_1}{x_2-x_1}$

Slope of the line passing through (8, 5) and (4, 10),

m = $\frac{10-5}{4-8}$

m = -$\frac{5}{4}$

Equation of line will be,

G = $-\frac{5}{4}t+b$

Since, point (8, 5) lies on this line,

5 = $-\frac{5}{4}(8)+b$

5 = -10 + b

b = 15

Therefore equation of the function will be,

G = $-\frac{5}{4}t+15$

Here slope of the function represents the $\frac{5}{4}$ gallons of gas is consumed to drive the car for one hour.