Question

Mr. Hess teaches third grade. For every day his class behaves well, he puts $1 in the class pizza party fund, which is a function of well-behaved days.
Which kind of function is the pizza party fund?

A. quadraticB. exponentialC. linearD. constant

Answer 1

You have a function that for every well-behaved day adds $1. Let's call x the well-behaved days and y the amount of money in the fund. We can then make a table that looks like this:

X (well behaved days) , Y (money in fund)

0, 0
1, 1
2, 2
3, 3
4, 4
5, 5

If you take these as points: (0,0), (1,1), (2,2) , ... and plot them you get a line. The relationship is linear.

Another way you can tell is that y = x which is the equation of a line with slope = 1 and y-intercept 0 although for this case we only focus on x values that are 0 or greater because there would not be a negative number of well-behaved days.

A third way you can tell is that the money in the fund increases by the same amount (1) for each well-behaved day. That is, it's rate of change is constant (always 1) and so it is linear...it has a constant rate of change or a constant slope.