 So a picture is worth a thousand words, an equation is essentially a bunch of words, a picture of that equation is a graph. When we graph an equation in two variables, we graph all ordered pairs x, y that correspond to solutions to the equation. So if I want to graph 3x plus 5y, we can't, since this isn't an equation. If I want to graph x squared plus y squared plus z squared equals 25, well, while this is an equation, there's three variables here, x, y, and c. And a little bit later on in the math sequence, you'll be able to graph things like that, but not quite yet. To graph 3x plus 5y equals 15, well, this is an equation. This does have two variables, and so we need to find all solutions to the equation. I don't know, finding all solutions sounds like it's going to be a lot of work. Let's find some solutions and worry about finding all solutions later. So rather than try to find all points on the graph, let's find a few, how about three points on the graph. And to do this, we'll employ a time-honored strategy in mathematics to solve a problem, change it into a previously solved problem. And we might begin with the observation, since we know how to solve equations with one variable, we'll try to make this into an equation with one variable. And one way to do that is to pick a value for one variable, and then replace and solve. So let's pick a value for y. How about y equal to... Well, how about zero? We like zero. Zero is a nice number to work with. If we let y equal zero, equals means replaceable, so every place we see a y will replace it with zero, our equation becomes, and now this is an equation with one variable, x, and we can solve for it. So we know that x equals 5, y equals zero, solves the equation. And if it's not written down, it didn't happen. So we want to record this point with the coordinates x value, y value. So x equals 5, y equals zero, and the point is 5, zero. Well, that was fun. Let's try to find another point. Well, how about this side? We'll let x equals zero. If we let x equals zero, equals means replaceable, so every time we see x, we'll replace it with zero, and that gives us an equation. And we can solve this equation, which will give us, and so x equals zero, y equals three, solves the equation. So x equals zero, y equals three is another point on the graph, and we can write that down and coordinate form zero, three. Well, we want another point, so we have to choose a value for either x or y. So maybe we'll choose x equals... Well, how about ten? That seems to be a nice, easy value to work with, and so equals means replaceable, so we'll replace every occurrence of x with a ten. We'll get a nice equation, and we'll solve it for y, and that tells us x equals ten, y equals negative three is a point on the graph, and so I'll record that as the coordinate ten, negative three. So let's graph these points. So first, we'll very carefully draw a big empty space, here it is, and some place we'll put our origin, about here, and x marks the spot. From the origin, we'll need to define two principal directions, and we'll have the one running to the right, and the other running upward. Now, once we've defined the two principal directions, this allows us to draw a grid that helps us to mark space. So let's draw that grid. To graph the first point, five zero, we'll start at the origin, and go five units to the right, and zero units upward. So here goes one, two, three, four, five units to the right, and don't move up or down. To graph zero three, we'll start at the origin, and go zero units to the right, and then three units upward. And finally, to graph ten, negative three, we'll start at the origin, and go ten units to the right, and three units downward. And that gives us the graph of these three points.