Graphing Lines in Slope-Intercept Form

In this problem we've been asked to graph the line Y equals two X minus three. This equation is written in what's called slope intercept form. Slope intercept form is right here, this Y equals MX plus B it's when the Y is by itself on the left hand side, the term with the X is first on the right hand side, followed by the constant term. When it's written in slope intercept form, you can look at the number in front of the X this is your slope of the line. The slope of a line is rise over run, but it tells you how steep the line is. And we can tell based on the sign of the slope what direction the line is going to go in. So if your slope is positive, that means your Y values are increasing as X increases. So it's going to go up to the right. If your slope is negative, that means your Y values are decreasing. So it's going to go down to the right. If your slope is zero, that just means your Y values are not changing. That's just going to be a horizontal line. And if your slope is undefined, it's a vertical line. So what I usually do when I'm graphing the line and sloping intercept form is I start with the B you can think of the B as where to begin on the graph. Where to start. The Y intercept is just where the line crosses the Y axis. So if we look at our equation, we have a minus three at the end. That tells us that RB value is negative three. So we can begin our graph going down three from the origin. So we're going to start at negative three on the Y axis. This is the Y intercept where it crosses the Y axis. The M is how to move to the next point on the line. So in our case, we have a two in front of the X, that means our M is two, our slope is two. It's positive. That means that my graph is going to be going up to the right. And I know that slope is rise over run. So it helps when you're graphing if your slope is written as a fraction. If it's not written as a fraction, you can always turn it into a fraction by just dividing by one. Dividing by one doesn't change this to divided by one is still two. So if I know my slope is a positive two over one, I'm going to be going up to the right, the two is the rise. So from this point, I'm going to go up to and the run is one going to go over one to the right. And if you want to do it again and get a couple extra points on your graph, you can. So I can go up to again over one. This gives me 3.7 my line. So all that's left to do for this one is to just draw a straight line that goes through these points. So here's the graph of Y equals two X minus three. I had a minus three, so we started down at negative three and the slope was a positive two, so we went up to over one. Let's look at one more. In this equation we have Y equals negative one fourth X plus two. So I would start with the Y intercept the B, it tells me where to begin on the graph. I have a positive two at the end so that means my B value is a positive two. That tells me I can begin the graph by going up to from the origin, so this is my Y intercept my graph crosses the Y axis at a positive two. The number in front of the X is a negative one fourth, that tells me that my M is negative one fourth. That's my slope. It's a negative, so that tells me my line is going to be going down to the right. And I can think of the one as the rise and the force, the run. So since it's negative, I need to go down one instead of going up one, and I'm going to go over four to the right one, two, three, four, so from the Y intercept my line is going down to the right, it went down one over four. If you want to do another point on there and going the other way, you can go up one, put then you'll have to make sure you go to the left for so that the overall direction of your line is going down to the right. So now on this line, all that's left to do is to connect the dots with a straight line. So this is the graph of Y equals negative one fourth X plus two, I started at two, that's my Y intercept. My slope was negative, so my line is going down to the right, and it's going down one over four.