Question

A moving company charges a one-time and a cost per mile for its service. The relationship between the mileage and the cost is displaying in the graph. Which equation best represents the relationship between the total cost, C, and miles traveled, m?*

Answer 1

This is a linear relation. For linear relations, we have the general form:

`y=ax+b`

Where 'a' is the slope and 'b' is the intercept.

In this problem, we have that the intercept b is 200, because that's the point where the line crosses the y-axis. For now we have something like:

`C=am+200`

(here y is C and x is m)

To find the slope we have to use the intercept point (0, 200) and another point on the line. We can see that one of those points is (200, 500).

For a line with points (x1, y1) and (x2, y2), the slope is find like:

`a=(y_2-y_1)/(x_2-x_1)`

In this problem, the slope is:

`a=(500-200)/(200-0)=(300)/(200)=(3)/(2)=1.5`

Then, we have the equation that represents the relationship between the mileage and the cost:

`C=1.5m+200`