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?

2 Answers
Jul 11, 2015

Answer:

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]}

Jul 11, 2015

Answer:

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#
# #
# #
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 #color(blue)5# hours, you will pay :

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