Point-slope form of a line is one method to write the equation of a line. Start with the slope equation, which is basically the difference between two points, and then rearrange the terms to obtain the point-slope form of a line. The point-slope form of a line provides a formula that is useful in finding the slope of a line from an equation and a point the line passes through.
Point slope form of a line is my personal favorite and it's the reason why is it's a really easy way for me to remember how to write the equation of a line. It all starts with the slope equation, which if you remember is, m is equal to change of y's over change of x's. Now what you have to remember about this is, this is basically the difference between two points. So we have the point x2,y2, we also have the point x1,y1. What we could do is actually replace one of those points with a new point, just drop the subscripts. So we could actually say that this is the same thing as, y is equal to, m is equal to y-y1 over x-x1. Same exact equation but instead of having the y2 and x2 we just drop the subscript and assume new set of points.
Okay, what we do here is we basically then cross multiply. We take our x-x1 move it to the other side, what we end up with then is x-x1 times m is equal to y-y1. Do a little bit of rearranging. Switch sides basically and we end up with y-y1=m, x-x1 and what this is is basically, m is still your slope and that what we have here is we have the point x1,y1 that is also on our line, okay? So point slope form of a line, just a different way of writing slope.