 This video is going to talk about linear equations in two variables, and we're going to learn a little bit about those kinds of equations. So the first thing we're going to learn is about x-intercepts and y-intercepts. Intercept sounds like when you cross something, so the x-intercept is when it crosses the x-axis. That would be this point right here. And then it is why I was going to have the point, we go across to the x-value, but then we don't go up or down, so it's always going to look like a0, some number and zero. Y is equal to zero. And for the y-intercept, it's where it crosses the y-axis, in this case it would be this point on this line. And again, we start at zero, zero. We don't go left or right in order to be able to find an y-axis. So we have to stay at the origin and then just go down. So it's going to have a zero and then some number for B for the y-intercept. So x is going to be equal to zero. So in an x-intercept, the y is always zero. In a y-intercept, the x is always zero. So the opposite variable is zero when you're trying to find an intercept. So now we want to just be able to graph. Now we talked about x and y-intercepts because they're very nice points. When you let a variable be zero, nice things happen. So let's look at this point. We have this equation and I'm going to let x be zero. And see if I can solve this equation. So x is zero. That means that I have negative y equal to negative eight. And if I divide by negative one, or y is going to be equal to positive eight. And then if I let y be zero, I would have 4x and then minus zero equal to our negative eight. And if we divide by our four, because this drops out, then x is going to be equal to negative two. So x is negative two, y was zero. So you can see that you can pick either an x or a y, it doesn't matter which one you pick. We just want to pick a point so we can find nice numbers, if at all possible. So since y is all by itself, I think I'm going to pick another x. Let's let x be, oh let's say one. So I'm going to come over here again and try. Four times one, which is x, minus y is going to be equal to negative eight. Well this time I have four, so I need to subtract four from both sides. So negative y is going to be equal to negative 12. And if I divide by negative one, then I'm going to end up with y is equal to positive 12. So we ended up with 12. So zero, eight, started zero and go up to eight. And this is six, seven, eight. So I just made my graph for that one. Negative two and then zero would stay on the x-axis. That would be our x-intercept. This would be our y-intercept. And then one, 12. Well that's going to be, this is eight, nine, ten, eleven, something like this. Okay, there's the point that I wanted. And if I draw my line, I can see that's about right. Okay, so now I've drawn my graph and I've used the intercepts to help me find that. Two points to find a line remember and the x-intercept and the y-intercept were two points. And then I just had to find a third point to make my graph more accurate. Let's try again. This time we have y and equal three x minus zero. So let's let x be zero to start off with. So y is equal to three times that zero which is x minus three. Well anything times zero is just zero so y is equal to negative three. Now let's let y be zero. So zero is equal to three times x minus three. So I'm going to add three to both sides and I'm going to end up with three equal to three x and when I divide by three to get x by itself then x is going to be equal to one. Now I just need to find one other nice point. Let's try negative one just to get a negative number in there. So y is going to be equal to three times negative one for x minus three. Well this is negative three minus three which is y. So y is going to be equal to negative six. So if we did it right all our points should lie on a line so let's try. Zero negative three would be this point right here. One zero we go across one and then we stay on the x-axis. So now we found the two intercepts and negative one negative six we're going in the right direction that would be this point right here and those do look like they lie on a line and now we've graphed our line. Now what happens if we have a line like this one? Y equal to hmm I don't have any x's but I could say that's the same thing as plus zero x. So let's try zero for x. So y is equal to two plus zero times zero which is really just y is equal to two. Now let's try one for x. So y is equal to two plus zero times one. Again this cancels out so y is equal to two and if I tried negative two I'd have y is equal to two plus zero times negative two and again y is equal to two. What this really means is y is always two. So let's see what that graphs. Zero two would be this point right here. One two would be this point right here and negative two and then up to two would be this point right here. So we can see that if we have a y equal equation with just one variable it's only one variable in that equation and it's a y equal to a constant we actually have a horizontal line. And if we have this example x is equal to negative four there's no y here but we could say plus zero y. On this case zero is always nice to multiply by so let's pick y values. Let's try zero. So x minus is equal to negative four that doesn't look like a negative four let's make it a negative four plus zero times zero which is y and we have x is negative four. Can you guess what's going to happen? Let's let x y be negative three. So x is equal to negative four plus zero times negative three zero times anything is zero. So x is you guessed it negative four. I could try six let y be six or let it be okay let it be six. X is equal to negative four plus zero times six which cancels out and x is equal to negative four. So negative four over here zero would be this point right here. Negative four negative three would come down one two three and over to negative four and up to six one two three four five six and you can see that now this time we only had an x in our equation and that gave us a vertical line up and down is a vertical line.