In 2000, the average cost of tuition for 4 years of college was 16200; and in 2005 the average tuition cost was 20100. What is the y-intercept?

You are given two different data points. If you use the year for x and the cost of tuition for y, your data points are (2000,16200) and (2005, 20100).

Now you just need to come up with the equation of the line which passes through those two points. There are plenty of ways to do this, but I'd approach it as follows:

First calculate the slope (a.k.a. gradient) of the line. Let's call it m. Can you do that?

Once you have the slope, m, you can write the line in point-slope form:

(y-y_0)=m(x-x_0),

where x_0 and y_0 are the coordinates of any point on the line (including either of the two points you already know). Once you substitute for x_0 and y_0, you can solve the resulting equation for y to get the equation in slope-intercept form:

y=mx+b

The value you get for b is your y-intercept.