Grace is comparing cell phone plans. a prepaid phone plan costs $0.20 per minute and has no monthly fee. a contracted phone plan costs $50 per month and $0.02 per minute. how will the graphs of the monthy costs of the two cell phone plans compare where x represents minutes purchased in a month?

The graph of the first plan is a straight line that starts at the origin
and slopes up at the rate of  20¢/minute.

The graph of the second plan starts high up on the y-axis, at the
point where  y=$50, and from there it slopes with a very gentle
slope of  2¢/minute.

The slope of the first graph is 10 times as steep as the slope of
the second graph, but they do eventually meet, at  x = 278 minutes.

The second plan may seem very expensive, especially since Grace
would need to come up with $50 every month just to keep the phone
working, even before she even uses it.  But if she expects to use it
more than 277 minutes in a month ... about 9 to 10 minutes each day,
then that one is actually the cheaper plan, because its minutes are
so much cheaper.