The essay will need to be in your own words of course, but the basic idea is to replace x with 0 and solve for y to get the y intercept. To get the x intercept, replace y with 0 and solve for x.
Here's an example
2x+5y = 10
Let's find the x intercept
2x+5y = 10
2x+5(0) = 10
2x = 10
x = 5 is the x intercept
Now we'll do the y intercept
2x+5y = 10
2(0)+5y = 10
5y = 10
y = 10/5
y = 2 is the y intercept
The x intercept is the location where the graph crosses the x axis. The y intercept is where the graph crosses the y axis.