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: 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)

(10 points)

Explanation:

Answer 2

Part A: To get an equation into standard form to represent the total amount rented (y) that Marguerite has to pay for renting the truck for x amount of days, we use the formula for the equation of a straight line.

Remember that the equation of a straight line passing through points is ( x_{1} , y_{1} ) and the points ( x_{2} , y_{2} ) is given by
y - y_{1} / x - x_{1} = y - y_{2} / x - x_{2}

Knowing that Marguerite rented a truck at $125 for 2 days, we know if she rents the exact same truck for 5 days, she has to pay a total of $275 for the rent.

This means that the line modeling this situation crosses points at (2, 125) and (5, 275).

The equation modeling the total rent (y) that Marguerite has to pay for renting the truck for x days is given by

y - 125 / x - 2 = 275 - 125 / 5 - 2 = 150 / 3 = 50

But if you are writing the equation in standard form it would be

50x - y = -25


Part B:
When writing the function using function notation it means you are making y the subject of the formula and then replacing the y with f(x).

If you remember that from part A, we have that the equation for the total rent which is y that Marguerite has to pay for renting the truck for x amount of days is given by
y = 50x + 25.

Writing the equation using the function notation would give us this
f(x) = 50x + 25


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