Question

Part A: Marguerite rented a truck at $125 for 2 days. If she rents the same truck for 5 days, she has to pay a total rent of $275.
Write an equation in the standard form to represent the total rent (y) that Marguerite has to pay for renting the truck 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)

Answer 1

PART A:
To obtain an equation in the standard form to represent the total rent (y) that Marguerite has to pay for renting the truck for x days, we use the fomula for the equation of a straight line.

Recall that the equation of a straight line passing through points $(x_1,\ y_1)$ and points $(x_2,\ y_2)$ is given by
$\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}$

Given that Marguerite rented a truck at $125 for 2 days. If she rents the same truck for 5 days, she has to pay a total rent of $275.
This means that the lne modelling this situation crosses points (2, 125) and (5, 275).

The equation modelling the total rent (y) that Marguerite has to pay for renting the truck for x days is given by,
$\frac{y-125}{x-2} = \frac{275-125}{5-2} = \frac{150}{3} =50 \\ \\ y-125=50(x-2)=50x-100 \\ \\ y=50x+25$

Writing the equation in standard form, we have
50x - y = -25


PART B:
Writing the function using function notation means making 'y' the subject of the formula and then replacing the 'y' with 'f(x)'.

Recall that from part A, we have that the equation for the total rent (y) that Marguerite has to pay for renting the truck for x days is given by y = 50x + 25.

Writing the equation using the function notation, we have
f(x) = 50x + 25


PART C:
To graph the function, we label the x-axis 'number of days' and label the y-axis 'total rent'. the x-axis is numbered using the intervals of 1 while the y-axis is labelled using the intervals of 50.
The points (2, 125) and (5, 275) are marked on the coordinate axis and a straight line is drawn to pass through the two points.