The slope-intercept form is one way to write a linear equation (the equation of a line). The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). It's usually easy to graph a line using y=mx+b. Other forms of linear equations are the standard form and the point-slope form.
Equations of lines have lots of different forms. One form you're going to see quite often is called the slope intercept form and it looks like this: y=mx+b, where m stands for the slope number and b stands for the y intercept.
So, when you're doing problems where you're asked to write the equation in slope intercept form, you only need two pieces of information. The first piece of information you need is the slope number and the second piece of information you need is the y intercept. Once you have those two pieces, those two numbers, you just plug them in there and you're on your way.