Question

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?

Answer 1

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*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]}

Answer 2

Cost = `25 + 8.5*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 `color(red)1` hour, you will pay `$8.50 = color(red)1xx$8.50`
If you play `color(red)2` hours, you will pay `$17=color(red)2xx$8.50`
If you play `color(red)3` hours, you will pay `$25.50=color(red)3xx$8.50`
.....
.....
Let `color(red)h` the number of hour(s) played, you will pay `color(red)hxx$8.50`
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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`
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For example, if you are not a member and you want to play `color(blue)5` hours, you will pay :

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