Answer:
![G=-\frac{5}{4}t+15](https://tex.z-dn.net/?f=G%3D-%5Cfrac%7B5%7D%7B4%7Dt%2B15)
Slope = ![-\frac{5}{4}](https://tex.z-dn.net/?f=-%5Cfrac%7B5%7D%7B4%7D)
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
and
is,
'm' = ![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Slope of the line passing through (8, 5) and (4, 10),
m = ![\frac{10-5}{4-8}](https://tex.z-dn.net/?f=%5Cfrac%7B10-5%7D%7B4-8%7D)
m = -![\frac{5}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7D)
Equation of line will be,
G = ![-\frac{5}{4}t+b](https://tex.z-dn.net/?f=-%5Cfrac%7B5%7D%7B4%7Dt%2Bb)
Since, point (8, 5) lies on this line,
5 = ![-\frac{5}{4}(8)+b](https://tex.z-dn.net/?f=-%5Cfrac%7B5%7D%7B4%7D%288%29%2Bb)
5 = -10 + b
b = 15
Therefore equation of the function will be,
G = ![-\frac{5}{4}t+15](https://tex.z-dn.net/?f=-%5Cfrac%7B5%7D%7B4%7Dt%2B15)
Here slope of the function represents the
gallons of gas is consumed to drive the car for one hour.