Question

The Frenchtown Roller Rink charges a $5 entrance fee and an hourly rate for roller skating. The total cost for roller skating depends on the number of hours a person skates. The table below represents the total cost of skating for different numbers of hours.Which Equation represents between the cost,c,and the number of hours,h?

Answer 1

`c=3h+5`

Explanation:

This situation can be represented by a linear function since it has a constant rate of change, linear functions are represented by the following equation:

`\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{rate of change} \\ b=y-\text{intercept} \end{gathered}`

To determine the rate of change of the function, we can use the following expression:

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

We have the following given points: (0,5) and (1,8):

`\begin{gathered} m=(8-5)/(1-0) \\ m=3 \end{gathered}`

The y-intercept is where the functions cross the y-axis, which means x=0.

In the table, we can see that the y-intercept of this function would be 5.

Therefore, the equation that represents this relationship between cost, c, and the number of hours h:

`c=3h+5`