Graph the given linear equation. y = 1 2 x − 2 y=\frac12x-2

This problem asks us to graph the given linear equation, y equals one half x minus two. Now what I'm going to do is sketch a graph. So we're going to have a y axis, then we're going to have an x axis. Now what I'm going to do is I'm gonna choose five units up, down, to the left, and right. So we'll start on the x axis, we'll go one, two, three, four, five. In the positive x direction, we'll go one, or I'll go one, two, three, four, five in the negative x direction. Then we're going to go five units up, one, two, three, four, five in the positive y direction, and then one, two, three, four, five in the negative y direction. So we've now sketched our graph. Now, typically, when I'm doing these problems where I need to graph a linear equation, I start with an x value of negative one. But I'm actually not going to do that in this video, because I noticed that the x that we choose is going to be multiplied by one half. So what I'm actually gonna do is be strategic about this, so that way I get whole numbers. Remember, you can choose any x values that you want to. And if you wanna start with negative one, if you're just comfortable starting with negative one, then zero, then one, then two, if you're comfortable with that, that's totally fine. But I'm actually gonna show you something different for this video. I'm going to start with an x value of zero. So I'm gonna start right in the center of our graph in an x value of zero, or in the center of the x axis, I should say. And that's going to allow me to take my x and replace it with zero. So we'll get y equals one half times zero minus two. Now anything times zero will just give you zero, so we'll get zero minus two, which is negative two. So we get the point zero, negative two, which gives me a point at x is zero and y is negative two. So we have one of our points plotted. Now what I'm going to do is rather than choosing an x value of one, which might seem like the next logical step, I can see that that's gonna be multiplied by one half, which is gonna give me a fraction. So instead, I'm actually gonna choose an x value of two next, and I'm specifically gonna try to choose even numbers here. So what I'm gonna end up with is y equals one half times two minus two, because notice by choosing two as my x value rather than one, the two's actually just cancel. One half of two is just one. So we get one minus two, which is negative one. So I know when x is two, y is negative one. So at an x value of two, we're going to get a y value of negative one, which will show up on our graph. Now we would have still gotten a point that showed up on our graph if we chose one, but we would have gotten a fraction, which would have been really ugly and hard to deal with. So that's why I chose actually, this should be an x value of two. Right? Two negative one. Yeah. So that's why I chose an x value of two, right about there. Now let's choose an x value of four. Notice I'm going by even numbers here, so we're gonna choose four where our x value is gonna be at this point. And what I'm gonna do is take my x and replace it with four. So we'll have y is equal to one half times four minus two. One half of four is just two because four divided by two gives us two minus two which gives us zero. So when we have an x value of four, we have a y value of zero zero, which puts us exactly on the x axis. So this would be our point zero or our point four zero. Now notice by drawing these points, we can actually sketch a line. It's not a very steep line, but it's gonna go through these points. So this is what our graph is going to look like, and that would be the solution to this problem. So this is how you can sketch a graph, and again, you can choose the x values that you want. When I choose negative one zero one two, that's oftentimes just a safe place for me to do because I know that those are values that are going to be in that region and the math's usually not too hard to deal with. But in situations where you see a fraction and you strategically know what's going to divide and give you whole numbers or cancel, you can predict that, and that's how you can sketch your graph. You can be creative with how you choose points like I was in this one. And, again, you could have chosen negative one, zero, one, and two, and you would have still gotten the correct answer. But often, remember, you can choose whatever x values you want to to get the y values as an output and to see what your graph is gonna look like. So this is how we can graph these linear equations. Hope you found this helpful.