Question

ben and julia rented a truck from the same company to move to college. ben drove 150 miles and paid $64.95 while julia drove 84 miles and paid $45.15. a) write an equation to model the total amount due, y, after driving x miles. b) what does the slope & y - intercept mean in terms of the problem? c) what is the cost per mile?

Explanation:

Step1: Find the slope (cost per mile)

The slope \(m\) of the line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x_1 = 84,y_1=45.15,x_2 = 150,y_2=64.95\).

$$m=\frac{64.95 - 45.15}{150 - 84}=\frac{19.8}{66}=0.3$$

Step2: Find the y - intercept (base cost)

Use the point - slope form \(y - y_1=m(x - x_1)\). Substitute \(m = 0.3,x_1 = 84,y_1=45.15\)

$$y-45.15=0.3(x - 84)$$

$$y-45.15=0.3x-25.2$$

$$y=0.3x+19.95$$

Step3: Interpret the slope and y - intercept

The slope \(m = 0.3\) represents the cost per mile. The y - intercept \(b = 19.95\) represents the base cost (the cost when \(x = 0\) miles are driven, i.e., the fixed cost of renting the truck).

Step4: Answer for part (c)

The cost per mile is the slope of the line. As calculated in Step1, it is \(0.3\) dollars per mile.

Answer:

a) The equation is \(y = 0.3x+19.95\)
b) The slope (\(0.3\)) is the cost per mile and the y - intercept (\(19.95\)) is the base cost of renting the truck.
c) The cost per mile is \(\$0.3\)