Question

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. Write an equation that represents the pricing plan.

Answer 1

A linear equation is given by:

`\begin{gathered} y=mx+b \\ \text{Let:} \\ C(d)=\text{Cost as a function of days} \\ d=\text{days} \\ b=y-\text{intercept} \\ C(d)=md+b \end{gathered}`
`\begin{gathered} \text{for:} \\ d=2,C(d)=105 \\ 105=2m+b \\ \text{for:} \\ d=10,C(d)=465 \\ 465=10m+b \\ \text{let:} \\ 2m+b=105\text{ (1)} \\ 10m+b=465\text{ (2)} \end{gathered}`

Let's solve this 2x2 system of equations:

`\begin{gathered} \text{From (1):} \\ b=105-2m\text{ (3)} \\ \text{ Replace (3) into (2)} \\ 10m+105-2m=465 \\ \text{solve for m:} \\ 8m=465-105 \\ m=(360)/(8) \\ m=45 \\ \text{ Replace m into (3)} \\ b=105-2(45)=105-90=15 \end{gathered}`

Therefore, the equation which represents the pricing plan is:

`C(d)=45d+15`