 In this video, I'm going to talk about graphing functions in slope intercept form. This is what I would say is the standard model is the standard way of graphing an equation. This is the one that was most traditionally used. There was, I did previous videos on graphing using intercepts and graphing using a point and slope. Those two methods are, they're useful but they're not used very much with equations. What we're going to do here is we're going to graph using slope intercept form. This is actually going to be very, very similar to the first video graphing using a point and slope because that's exactly what we're going to use. We're going to use a single point and then we're going to use slope to figure out where to go from there. I'll try to make that connection as I go through. Graphing functions using slope intercept form. I want to write the function negative 2x minus y equals 3 in slope intercept form and then graph the function. Whenever you have an equation, this is a linear equation, it's in standard form. How do I know it's in standard form? Here's the equal sign, x's and y's are on the left side. That tells me it's in standard form. Number's on the right, x's and y's on the left. Now we're in standard form, but standard form is not slope intercept form. I have to take this equation, change it to slope intercept form and then graph it. What is slope intercept form? This is something that you should memorize. Slope intercept form is y equals mx plus b, y equals mx plus b. Why do we call it slope intercept form? Because right here, that's the slope and right here, the b, that is your y-intercept. Notice some of the vocabulary there, y-intercept. If you remember back to a previous video of mine, we talked about x and y-intercepts. Actually if you have an equation in this form where y is by itself, this last, this number portion over here, that tells you what the y-intercept is going to be. Keep that in mind as we go through this. Again, we want to change this equation into slope intercept form. We want to get the equation to look like this. Basically, we want to get y by itself. I'm going to rewrite this equation. Negative 2x minus y equals 3. I'm going to use a little bit of algebra to solve this. Now this method only works if you solve for y. You have to get it by itself. There's no way around that. So you've got to use a little bit of algebra to do that. So I see a negative 2x. I'm going to add it over to the other side, equals 2x plus 3. I took this and added it over to the other side, making it a positive 2x. Remember, these don't combine. This is a number. This is a variable. These are not going to combine. So other than that, now you might think, OK, one step and I'm done. Well, wait a second. We got this negative right here, which means I've got to get rid of that too. It needs to just be y that I'm looking for. So basically, another easy way to look at this is change the sign on this side. If I change the sign on this side, I've got to change all the signs on the right side. So it's negative 2x minus 3. See how we did that? Change the sign right here, and then we changed all the signs over here. Positive became negative negative. That's kind of the easy way to do it. Technically, what we did there is we divided everything by a negative 1. So that's technically what we did. Also, multiply by negative 1 does the same thing. But anyway, the goal was to get y by itself, and that's what we have done. So now from this, there's a couple of different things that we can find right here. Right here, that negative 2, that tells you what the slope is. So my slope is negative 2. Again, the m part of it is slope. Now the y part of it, the y intercept, the y intercept is negative 3. Now these two pieces of information are going to help me to graph. These two pieces of information are going to help me to graph. So the b there, sorry I forgot to note that, negative 3 is the b is the y intercept. So you could also say that b is equal to negative 3. Either way, you can look at it either way. But anyway, all right, moving on. Those two pieces of information will help me. Now again, I'm going to kind of refer back to my first video, graphing with a point and slope. So now what we have here is we have a point. This right here, this y intercept, that is a point, and then we have a slope of negative 2. Now right here, you might think to yourself, well, Mr. Man, that's not a point. There's only one number there. Coordinates, points, they have two numbers. They have an x and a y. Now, well, you're absolutely right. But remember, this is a y intercept. So that tells us where the line is going to intercept the y-axis. So what I'm going to do is I'm going to take that, bring it over here. Here's the y-axis. And so negative 3 is where my line is going to intercept. So that's right here. You know what? Let me do the correct coloring. Let me undo that real quick. So one more time, negative 3 is the y-intercept, which is right here. There we go, a little good color there. All right, so that is where my y-intercept is at. Now from that point, I'm done with the y-intercept. I'm going to use that to find more points that are on that line. So now I'm going to come over here and I'm going to look at the slope. I'm going to come over here and I'm going to look at the slope. I have a slope of negative 2. Now remember, slope is rise over run. So that negative 2 is actually negative 2 over 1. We have to look at it as a top and a bottom number so I can get a rise of 2 and I can get a run of negative 1. Just keep that in mind. So from this point, so I'm going to take this slope over here, negative 2 over 1. From this point, I'm going to have a slope of negative 2 over 1. So a negative slope looks kind of like this. That's not the actual line, but that's what the line should look like, look something like that. So now when I create more points for my line, I need to either go up into the left or I need to go down into the right. Rise and then run, rise and then run. I have to go in those two directions. OK, so let's get rid of this. Let's actually create the line I want. So again, slope of negative 2 over 1, I'm going to rise 2, 1, 2, and I'm going to run 1. So right there. Rise 2, 1, 2, run 1, right there. Now as I said in previous video, you need to make three points to create your line. Minimum of three points. Actually technically it's a minimum of two, but I want you to create three points so that you check to make sure you're doing your slope correctly. It's just a failsafe for you to make sure you're doing this correctly. I could also go down with this. I could rise 1, 2, and then run 1. I could also do that. So now I got four points, which is fine. A little bit of excess for me, that's OK. Now connect all the dots, get as straight as I can line there, and this is my linear function. This is my line that I have. So this line right here is negative 2x minus y equals 3. Or, let me use a little bit different color here, or you could call it y equals negative 2x minus 3. Those are the two equations I have there. They're the exact same equation. They're just written differently. One of them is written in standard form. The other one is written in slope-intercept form. But that's what the line looks like. So that's it. I'm done. That's all I really need to do. So to recap on this just a little bit, graphing, if I want to graph a function in slope-intercept form, the first thing I need to do is write the function in slope-intercept form. So what I have to do is get y by itself. So if you have an equation, make sure that y is by itself. If it's not by itself, then you need to do a little bit of solving to figure out what the equation is. So there's my equation. Once I have figured that out, then I take the slope and the y-intercept. And I use those two, the y-intercept and the slope, to create my line. So that is the summary of what we did, a quick summary of what we did. All righty. That is graphing functions in slope-intercept form. Hopefully this video was informational and helpful for you. And thank you for watching.