Sometimes we're only given a couple of points on a line and then asked to write a linear equation. When given this information, it's easiest to use point slope form. Point slope form can be written using one point and the slope or when given two points since we can calculate the slope from the two points. Once we have an equation in point slope form it can be rewritten in slope-intercept or standard form.
The same equation for a line can be written in lots of different ways. You guys are probably already familiar with the point slope formula, which is what we're going to look at here today. The point slope form of an equation of a line looks like "y-y1=m(x-x1)" where m is the slope and "x1, y1" is a point on the line.
These little subscripts, those little 1's are just to show that we're representing a point. It's different from the y value and the x value. These guys in your answer are going to stay as the letters x and y. These little ones with the subscripts are going to become numbers.
The point slope form is not terribly useful by itself. Most of the time it's used as a way to get to slope intercept form.
You'll see more what I am talking about once you start doing some examples. But keep in mind this is a great way to start especially if you're given a point and a slope, hence the name.