- OK. So what, again, we have is we have two points here. And we want to write the equation of the line. And we're going to use point-slope form because point slope form can help us use two points. Now, in my last problem, I showed you how to find the slope. And we could just plug them into equation. We could also just look at this and say, all right, well, I want to label these. Whenever we have my two points, I know that these are both x and y-coordinates. And I'm going to label them x1, y1, and x2, y2. 

And a lot of you are probably familiar with the slope formula. So rather than plugging them into this equation and finding the slope, we can easily just write them into the equation of the slope formula. So the slope formula, remember, is m equals y2 minus y1 over x2 minus x1. So therefore, all this-- let's go ahead and figure this out here real quick. 

So I have negative 2 minus 6, all over 2 minus a negative 4. Well, negative 2 minus 6 is going to be a negative 8. Negative 2 minus a negative 4 is going to be a double positive-- so that will make it positive-- over 6, which equals-- divide-- you'll have a negative 4/3. So now we know m equals a negative 4/3. 

So when writing my equation using my point-slope form, I'm going to now a negative 4/3 in for m. But the next thing is, we know that we're going to put that in for m. But then we need to determine, well, what other point can we plug in? Now, before, I showed you how to write it in slope-intercept form, where we're just given one point and the slope. Well, now we're given two points. So we need to determine, which point do we pick? And it doesn't matter because it's going to be true for all points that lie on the line. 

So since these are the two points that we're told are on the line, we can choose either one. And it looks like to me-- I guess it really doesn't matter. Let's do x2 and y2. So if I wanted to rewrite this equation, rather than writing it as y minus y1 equals m times x minus x1-- I know it gets a lot of students confused because they say, well, you're going to use this point. Well, then that's fine. Let's rewrite it like this. 

It doesn't matter which y's and x's I use. You can just rewrite it. It's going to be the same thing for either point. So therefore, I have y minus a negative y2 equals-- now a negative 4/3 times x minus 2. 

All right. So now what I can do is I can apply my distributive property. And then that turns into a positive y plus 2 equals a negative 4/3 x. And this becomes now a positive 8/3. 

Now I'm going to subtract 2 on both sides. So now I have 8/3 minus 2. And I'm going to change that over to 1 because now I got to combine them by getting the same denominators. So to get the same denominators, I need to multiply by 3/3. So therefore, I have 8/3 minus 6/3, which equals 2/3. 

So therefore, my final equation in slope-intercept form is y equals a negative 4/3 x plus 2/3. So there you go, ladies and gentlemen. That is how you write an equation between two points in slope-intercept form. Thanks