How to Graph Linear Equations

Video Transcript

"Hi, I'm Steve Jones, I'm going to show you how to graph linear equations. First of all, here is the linear equation, very simple one, y=x 3. So, y is the variable, x is the other variable and 3 is the constant. So our first task is to define values of x. So I've started, x-3, -2, -1, 0, 1, 2 and 3. Maybe when you do this first time, you'll find you have to adjust it somewhat to make sure you get good values for drawing a graph. Once we have the value of x from -3, we put x-3 in the equation; y is -3 3 which of course is 0. Then, -2 in the equation, y is -2 3, gives us 1. And we work out the y values for each of the x values. And now we have a simple task to design axis. We have two axis, an x axis and a y axis. Now on the x axis, I go from -3 to 3. So I got, -1, -2, -3; 1, 2, 3. Vertically on the y axis I have no negative numbers, but if I did I would have to draw a line downwards. But I have, I start at 0, and I got, 1, 2, 3, 4, 5, 6. So I did 1, 2, 3, 4, 5, so this will be a value 6. Now I simply take this points, we call this point co-ordinates, these are called co-ordinates. Now the co-ordinates come in pairs, there's an x value and there's a y value. This is the x value, this is the y value. So these coordinates represent a points on this graph. Here, x is -3, well x is -3 anywhere on this line, x is -3. And at this time, y is 0. So the only place where x is -3 and y is 0, this is y, 0, is actually here; so I draw a point there. The next set of coordinates are x is -2; y is 1. Well x is -2 is this line and y is 1 is a line here. So in fact, this is that point. This is the point with coordinates, -2, 1. Here, when x is -1; y is 2, I again look at y is 2, and here is x-1 and I put another line on. Again x is 0; y is 3, so now you can see the pattern that we're getting in each case, x is now 1, y is 4; 2, y is 5; and 3, y is 6. And if you look at those, you will see that it is very easy to draw a straight line through those points and that is typical a linear equation will produce a line through the points when represented on an x, y graph of this kind."