Answer:
[tex]G=-\frac{5}{4}t+15[/tex]
Slope = [tex]-\frac{5}{4}[/tex]
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 [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of the line passing through (8, 5) and (4, 10),
m = [tex]\frac{10-5}{4-8}[/tex]
m = -[tex]\frac{5}{4}[/tex]
Equation of line will be,
G = [tex]-\frac{5}{4}t+b[/tex]
Since, point (8, 5) lies on this line,
5 = [tex]-\frac{5}{4}(8)+b[/tex]
5 = -10 + b
b = 15
Therefore equation of the function will be,
G = [tex]-\frac{5}{4}t+15[/tex]
Here slope of the function represents the [tex]\frac{5}{4}[/tex] gallons of gas is consumed to drive the car for one hour.
