Question

Part A: Sam rented a boat at $225 for 2 days. If he rents the same boat for 5 days, he has to pay a total rent of $480.Write an equation in the standard form to represent the total rent (y) that Sam has to pay for renting the boat for x days. (4 points)Part B: Write the equation obtained in Part A using function notation.(2 points)Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)the ons

Answer 1

We have the following:

Part A:

The form of the equation of a line is

`y=mx+b`

Where m is the slope and b is y-intercept

The first thing is to calculate the slope of the equation

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \end{gathered}`

The points are (2, 225) and (5, 480)

`\begin{gathered} m=(480-225)/(5-2) \\ m=85 \end{gathered}`

Now, for b:

`\begin{gathered} 480=85\cdot5+b \\ b=480-425 \\ b=55 \end{gathered}`

The equation is:

`\begin{gathered} y=85x+55 \\ \text{equation in the standard form} \\ y-85x=55 \end{gathered}`

Part B:

`f(x)=85x+55`

Part C:

To make a graph of the situation, we must give x values and evaluate them in the previous function.

For example

`\begin{gathered} f(1)=85\cdot1+55=140 \\ f(2)=85\cdot2+55=225 \\ f(3)=85\cdot3+55=310 \\ f(4)=85\cdot4+55=395 \\ f(5)=85\cdot5+55=420 \end{gathered}`

These points are plotted on the Cartesian plane, where the x-axis represents the days and the y-axis represents the total cost of the rent.