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:
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
is given by:
[tex] \frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1} [/tex]
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,
[tex](x_1,y_1)=(3,43)[/tex] and [tex](x_2,y_2)=(8,113)[/tex]
Thus, the equation of the line is given by:
[tex] \frac{y-43}{x-3} = \frac{113-43}{8-3} = \frac{70}{5} =14 \\ \\ y-43=14(x-3)=14x-42 \\ \\ y=14x+1[/tex]
Therefore, the equation of the line in standard form is
[tex]14x-y=-1[/tex]
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:
[tex]y=14x+1[/tex]
Therefore, the equation obtained in Part A written using function notation is given by:
[tex]f(x)=14x+1[/tex]
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.
