Couple of quick questions for a math guru

[Kreaper]

My 7th grade daughter is having trouble with basic algebra. She is just not that good with math and it has been... well, it has been a very long time for me. I was able to figure out all of the equation type questions, but I am stumped by a couple of others. The setup for the problems is:

The school drama club is performing a play at the community center. Props cost $250 and the theater is charging $1,25 for each ticket sold. So, the total cost C for the drama club to put on the play is C = 1.25n + 250, where n is the total number of tickets sold. Tickets are $4 each, so the total amount collected from sales is T = 4n.

1) What information does the y-intercept tell you about the income and cost for the tickets?

2) What information does the rate of change tell you about the income and cost for the tickets?

Coming up with equations to answer the rest of the questions was easy. I am drawing a blank on these though.

Thanks!

[Rawel_San]

In this case the y-intercept tells you the nonscaling costs of the production (i.e. the amount paid for props) where as
the rate of change tells you cost per ticket (what the theatre charges). If this is a way the problem is phrased in the
book it's rather misleading since they are asking about something they tell you thus making it confusing.
Especially since they don't point out they are talking about the rate of change and y-intercept of the function
of cost depending on the number of tickets sold.

[Krelar]

Just to generalize a little more, the y intercept of a function is going to tell you the initial or starting amount.

Even if no one comes to the play they still have to pay the $250 for props.

The sales equation on the other hand has a y-intercept of 0 so if no one shows up they won't make any money.

The rate of change is just what it says, a rate. In this case it is cost per ticket.

If you had an equation that told you how many miles you could drive for a given number of gallons of gasoline the rate of change would tell you the miles per gallon.

[Kreaper]

Thanks a lot guys! Actually, Rawel, this is from a worksheet. For some reason, they rarely use their text books. A book would probably have made this a bit easier. Thanks again guys!