 A very important and useful skill is the ability to write the equation of a line, and this goes back to a fundamental idea. An important skill for success in mathematics is learning how to navigate this transition between algebra and geometry. And this doesn't mean having past geometry go to take algebra, but really it means being able to convert an idea in algebra to an idea in geometry, or for an idea in geometry to an idea in algebra. So in this case, a line is a concept from geometry, an equation is a concept from algebra. And when we go back and forth between the equation of a line and the graph of a line, we're navigating this transition. So there's a number of ways of writing the equation of a line, but only one of them is actually important. Well, there's two, but only one of them is really that important. The line passing through a point hk with slope m has equation given by this, y equals m x minus h plus k. Now this I have my x and y coordinates of the point on the line hk. I have the slope of the line m, and there's my equation. And I don't really need to know anything else about how to write the equation of a line, because every other way of writing the equation for a line comes back to this one. So for example, let's write the equation of the line passing through the point five three with slope negative one third. So again, I can write down the equation. I have the line passing through the point hk with slope m, I can write down the equation. And again, paper is cheap. And let's go ahead and transcribe this information. So now I have the equation. And now I can compare what I want to get with what I have. So let's see. The point is hk. Here's the actual point. So that says that h is the same as five. So I'll go ahead and start substituting those in. H is five. That's my x coordinate of the point. So I'll substitute that in k. That's the y coordinate of the point. That's going to be three. So I'll substitute that in. And then m, that's my slope m. So slope is negative one third. I'll substitute that in. And there's my equation of a line. And I can do other things with this at this point. I can rewrite it. I can expand it. I can do lots of stuff with this. But really anything I do after this point is in the nature of arithmetic. And as far as the equation of a line is concerned, that's all I need. Because everything I need to do after this point, I can do with this equation.