# How do you translate the cost of playing tennis is $25 for a membership plus$8.50 per hour on court into an algebraic expression?

Jul 11, 2015

You can write this as a linear function in slope-intercept form.

#### Explanation:

Let's call $x$=hours on court and $y$=what you pay.

If you don't use the court ($x = 0$) you still pay $25, so $25$is your $y$-intercept. For every hour you play, $y$is upped by$8.50, so $8.5$ is your slope.

The expression then becomes:
$y = 8.5 \cdot x + 25$ with $x$ in hours and $y$ in $. The graph below is in 10's of$ to make it scale better. (of course the part left of the $y$-axis is nonsensical in this case)
graph{0.85x+2.5 [-5.24, 23.24, -2.4, 11.84]}

Jul 11, 2015

Cost = $25 + 8.5 \cdot h$

#### Explanation:

Imagine, just a moment, that the membership is free.
You only pay the number of hour(s) on court.

If you don't play, you pay nothing.
If you play $\textcolor{red}{1}$ hour, you will pay $8.50 = color(red)1xx$8.50
If you play $\textcolor{red}{2}$ hours, you will pay $17=color(red)2xx$8.50
If you play $\textcolor{red}{3}$ hours, you will pay $25.50=color(red)3xx$8.50
.....
.....
Let $\textcolor{red}{h}$ the number of hour(s) played, you will pay color(red)hxx$8.50     But the membership isn't free... Whatever the number of hour(s) you play, you must pay$25 for a membership.

Therefore : Cost = $25 + hxx$8.50



For example, if you are not a member and you want to play $\textcolor{b l u e}{5}$ hours, you will pay :

Cost = $25+color(blue)5xx$8.50=$25+$42.50=\$67.50