Hey, everyone. So up until now, when we've seen equations with 2 variables, their graphs were already given to us. For example, we saw that x+y=5 was a line that looks like this. But sometimes their graphs aren't going to be given to us, and you're going to have to go graph them yourself. That's what I want to show you how to do in this video, and, basically, the way we're going to do this is by plotting points. To graph an equation, we're going to calculate and plot a bunch of ordered pairs that make the equation true, and the way we do that is by plugging a bunch of x-values into this equation, and we're going to get points out of it. So those points we can take and plot them on a graph and then connect them with a line. That's basically what I'm going to show you how to do in a step-by-step way. Let's get started.
Alright. So we're just going to actually dive right into our equation or our example here so I can show you how this works. So we're going to graph this equation -2x+y=-1, and we're going to do this by creating a bunch of ordered pairs using some x-values that are already chosen for us. So here's the first step. You're going to take an equation, and if it's not already isolated to one side, you're going to have to isolate y to the left side. So, basically, you always want y= and then the rest of the equation on the right side. And the reason to do this is because you're going to plug x-values into this equation, and it's just going to be way easier to see what y is if it's isolated. Alright? So how do we do this? How do I take this equation over here and isolate y? Well, basically, all I have to do is just take the 2x, the negative two x, and move it to the other side. So I'm going to add 2x over here and add 2x to both sides. And, basically, what I end up with when I bring it down here, this is actually just going to end up being 2x-1. So now that y is isolated, I can move on to the next step.
What I want to do is I want to calculate y values for a bunch of x values that I choose, and usually 3 to 5 is enough. So, I've got my table here that we've got a bunch of x-values that are already chosen for me, -2 and so on. And what I'm going to do here is I'm just going to replace the x inside of this equation with whatever that x-value is, and then I'm basically just going to get a y-value out of it. So, for example, I'm just going to take this -2, and I'm going to plug it in. Right? So this is going to be 2×-2-1. So what does that give me? What y-value does that give me? Well, 2×-2=-4, and -4-1=-5. So this is going to be -5 over here. What that means here is that I plugged in -2, and I got out of it -5. So that's an ordered pair. The ordered pair that satisfies this equation is (-2,-5). You're just going to repeat this a bunch of times over here. So that's what we're going to do.
So this y=2×-1-1. So this is going to be -2,-1, which is going to be -3. So this is going to be (-2,-3). 0 is always a pretty easy point to do because usually what happens is you just replace x with 0 and one term just kind of goes away. So this whole term just cancels out, and then you get the -1, which is just -1. So the ordered pair is (0,-1). And then over here, we're going to get 2×1-1, so that's 2-1, and that's just going to give us 1. So this is going to be (1,1). And then finally, we've got 2×2,4-1=3. So the ordered pair is (2,3). Alright? So you just have to basically just plug and chug a bunch and fill out your table. Tables are going to be really good at organizing your information.
The third thing you're going to do is you're going to plot these xy points that you've just gotten in this table over here, and you're going to plot them on your graph. So let's go ahead and do that. So I'm going to take the ordered pair -2,-5, and that's going to be right over here. I'm going to take the points I'm sorry. This is going to be well, whoops. That's going to be -1. I'm sorry. Hopefully, you caught that. So -1,-3 is going to be this point over here, then we've got 0,-1. So that's over here. And we've got 1,1, which is over here. And then finally, we got 2,3 over here. So I just end up with a bunch of points, I'm going to plot them all, and the last thing I do is connect them with a line or sometimes a smooth curve. In this case, what happens is I can actually plot a line that goes through all of these 5 points, and so this is the graph of the line. So this is the graph of the equation, y=2x-1 or -2x+y=-1. That's how to graph these types of equations. The very last thing I want to sort of mention here is that most of the time these x coordinates won't be given to you, and if you're not given x values to evaluate, then you can always just feel free to choose your own. And usually, 3 to 5 is enough. Alright? So thanks for watching. That's it for this one.