Question

Johnathan rented a car from Hertz for two different trips. On his first trip he drove 88 miles and it cost him $428. On his second trip it cost him $673 to go 158 miles. Create an equation for renting a car from Hertz. How much would it cost him if he drove 388 miles?

Answer 1

The equation for renting a car is ;

y = 3.5x + 220

where y is the rental cost and x is the number of miles driven

The cost of rising 388 miles is $1,578

Explanation:

88 miles cost $428 while 158 miles cost 673, now we want to create an equation that represents renting a car from Hertz

We can make this in form of a plot with us having 2 data points here.

let the value y represent the cost of driving and x represent the number of miles driven.

So the kind of relationship we want to establish is a linear one that looks like ;

y = mx + c

Now let’s calculate the slope m with the two data points

The two points are; (88,428) and (158,673)

So the slope would be; (673-428)/(158-88) = 245/70 = 3.5

So what is left is the y intercept. To find this , we can make use of any of the two data points

Let’s say (88,428) in this case , so we have

528 = 88(3.5) + c

c = 528-88(3.5) = 528 - 308 = 220

So this means that our equation takes the form;

y = 3.5x + 220

where y represents the cost of traveling and x represents the number of miles driven

Now to the second part of the question, we want to know the cost of driving 388 miles

Just substitute the value 388 into the equation

y = 3.5(388) + 220

y = 1358+ 220 = $1,578