Question

Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113. Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours.
Part B: Write the equation obtained in Part A using function notation.

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.

Answer 1

PART A:
Recall that the equation of a line in standard form is of the form:
ax + by = c
where a, b, and c are constants.

The equation of a line passing through two points:
$(x_1,y_1)$ and $(x_2,y_2)$
is given by:
$\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}$

Given that Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113.

Thus,
$(x_1,y_1)=(3,43)$ and $(x_2,y_2)=(8,113)$

Thus, the equation of the line is given by:
$\frac{y-43}{x-3} = \frac{113-43}{8-3} = \frac{70}{5} =14 \\ \\ y-43=14(x-3)=14x-42 \\ \\ y=14x+1$

Therefore, the equation of the line in standard form is
$14x-y=-1$


PART B:
To write the equation with a function notation, we first express y in terms of x and then change y notation to f(x) notation.

Recall from part 1:
$y=14x+1$

Therefore, the equation obtained in Part A written using function notation is given by:
$f(x)=14x+1$


PART C:
To graph the equation obtained above, we draw the x- and y- axis with the x-axis labelled 'number of hours' and the y-axis labelled 'total rent'.

Next, we choose appropriate scales for x- and y- axis. Depending on the size of your graph book, you can choose an interval of 1 unit for the x-axis and an interval of 10 units for the y-axis.

From part A, we know that the line of the equation passes though points (3, 43) and (8, 113), mark these points and draw a straight line passing theough these points.