Question

ASAP help please and thankyou A rental car company has a linear pricing plan. The total cost C , to rent a car for 2,4,6, and 10 days, d, is shown A )What is the daily rate for the pricing plan? B) Write an equation that represents the pricing plan.

Answer 1

We are given a data set, and we are told that this can be represented as a linear equation. Let's remember the general form for the equation of a line:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept. To find the slope we use the following formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

where:

$\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}$

Are points through which the line passes. These two points can be found in the given data set. Let's take the following points:

$\begin{gathered} (x_1,y_1)=(2,105) \\ (x_2,y_2)=(4,195) \end{gathered}$

We can find the slope using the previous formula, like this:

$m=\frac{195-105}{4-2}=\frac{90}{2}=45$

This is the daily rate for the pricing plan. Now we can find the y-intercept "b" using one of the points given, like this:

$y=45x+b$

replacing the point (2,105), we get:

$105=45(2)+b$

Solving the operation:

$105=90+b$

subtracting 90 on both sides:

$\begin{gathered} 105-90=90-90+b \\ 15=b \end{gathered}$

Replacing the value of "b" in the equation:

$y=45x+15$

This is the equation of the line that models the data set given.