Question

An online clothes delivery service charges a flat fee for joining in addition to a monthly subscription cost. The graph shows the relationship between the number of months, , and the total cost, f(x).

Answer 1

To find the equation of the line shown, we need two points:

`\begin{gathered} (x_1,y_1)=(0,100) \\ \text{and} \\ (x_2,y_2)=(20,200) \end{gathered}`

The equation of the line goes by:

`y-y_1=m(x-x_1)`

The find m, the slope, we use the formula below and find m.

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1)_{} \\ m=(200-100)/(20-0) \\ m=(100)/(20) \\ m=5 \end{gathered}`

Now, let's put the point and m to find the equation:

`\begin{gathered} y-y_1=m(x-x_1) \\ y-100=5(x-0) \\ y-100=5(x) \\ y-100=5x \\ y=5x+100 \end{gathered}`

Changing to functional notation, this will be:

`f(x)=5x+100`

2nd answer choice is correct.