Question

A small college opened in 1999. In the linear model below, x represents the number of year after 1999, and y represents the student population. Interpret the slope. y=576+173x

Answer 1

So what need to do is find the slope. The equation for that is Y=mx+b. well thats the equation listed in your question, just its put a little different that the original format. Lets rearrange your stated equation ( We are allow to rearrange it however we want, but only on the right side of the equal sign, because its addition and will come out just the same.) 

So lets change it to Y=173x+576. That is your slpe. whatever value you enter for X, it will get multiplied by 173, then add 576. So in year 2000 (x value) the equation would be,
Y=173(2000)+576
Now, anytime you have a number with a x, y, z or any letter or a input value, such as 390x, when you enter the value for x it is multiplied. which is the same as putting it in parenthesis, 390(x) is that same as 390x. 
So lets multiply
Y=346,000 + 576
Y=346,576
Now plug in x=2001
Y=173(2001) + 576
Y=346,173 + 576
Y=346,749

Seems to me that every year the college is gaining 173 students. So as x goes over 1, y goes up one making the slope 1 over 173, or 1/173

Answer 2

There is a 173 increase in the student population per year after the college was opened.