SOLUTION: Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $88 for 180 miles. On another day she

Question 1171005: Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $88 for 180 miles. On another day she rented a car from the same agency and paid $151 for 360 miles. Find the linear function f(x) (where x is in miles and f(x) is in dollars) that the agency could use to determine its daily rental charges
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the general form of the linear equation is y = mx + b
y is the total cost.
x is the number of miles driven.
m is the slope.
b is the y-intercept.
the y-intercept is the value of y when the value of x is equal to 0.
the slope is equal to (y2 - y1) / (x2 - x1).
(x1,y1) and (x2,y2) are data points on the line of the equation.

you have two data points to work with.
they are:
(180,88)
(360,151)
these are in (x,y) format.
for example, (180,88) means y = 88 when x = 180.

assign one of these points to (x1,y1) and assign the other point to (x2,y2)
i assigned (180,88) to (x1,y1) and (360,151) to (x2,y2).
m = slope = (y2-y1)/(x2-x1) = (151-88) / (360-180) = 63 / 180 = .35
y = mx + b becomes y = .35 * x + b

to find the value of b, replace x and y with the value from one of the points.
i chose (360,151).
y = .35 * x + b becomes 151 = .35 * 360 + b
solve for b to get:
b = 151 - .35 * 360 = 25
y = .35 * x + b becomes y = .35 * x + 25

your equation is y = .35 * x + 25.
when x = 0, you get y = 25
when x = 180, you get y = .35 * 180 + 25 = 88.
when x = 360, you get y = .35 * 360 + 25 = 151
the equation is confirmed to be good.

your solution is that the linear equation used to determine its daily rental charges is y = .35 * x + 25.

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