Question

Enter an equation that gives the cost of renting a car for x days from Rent-AIL.The equation is y = ?

Answer 1

We want to find an equation that gives the cost of renting a car for x days from Rent-AIL. We are given the table with the total cost for 3, 4, 5 or 6 days.

We will assume that the values are in a linear relationship, and thus we will use two of the data given as points of the cartesian plane for finding the the equation. We have that for 3 days the cost is $49.50, and the corresponding point will be:

`(3,49.5)`

And for 4 days the cost is $66, the point will be:

`(4,66)`

We will find the slope of the line that passes through those two points, with the formula:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(66-49.50)/(4-3)=(16.5)/(1)=16.5 \end{gathered}`

And the slope will be 16.5. Now we will find the y-intercept,

`\begin{gathered} y=mx+b \\ 66=(16.5)(4)+b \\ 66-66=b \\ 0=b \end{gathered}`

This means that the y-intercept is 0, and thus, the equation that gives the cost of renting a car for x days from Rent-AIL is:

`\begin{gathered} y=mx+b \\ y=16.5x \end{gathered}`