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:
[tex](3,49.5)[/tex]
And for 4 days the cost is $66, the point will be:
[tex](4,66)[/tex]
We will find the slope of the line that passes through those two points, with the formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{66-49.50}{4-3}=\frac{16.5}{1}=16.5 \end{gathered}[/tex]
And the slope will be 16.5. Now we will find the y-intercept,
[tex]\begin{gathered} y=mx+b \\ 66=(16.5)(4)+b \\ 66-66=b \\ 0=b \end{gathered}[/tex]
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:
[tex]\begin{gathered} y=mx+b \\ y=16.5x \end{gathered}[/tex]
