Learn about Graphing Lines In this lesson, let’s learn how we graph lines when an equation is given to us. We’ll do two different problems. First one here’s the equation. y=(3/2)x+3. What is the line formula y=mx+b. B is the Y intercept, M is the slope. So what are the given. Slope equals mx so slope is 3/2 and we’re given the Y intercept equals plus b, here, b is three so we’re given the slope and we’re given the y intercept. What else are we given nothing else right? So here’s what we know if the Y intercept is three that means the Y intercept looking at the graph this is three that means the line cuts the Y-axis at three. What’s the coordinate here? That means the coordinate of a point is zero and three. Y equals three X is zero because at the Y intercept the value of X has to be zero. So what do I know? I know the common point zero and three. So first thing we do is we plot this point zero and three. Then, what we know is slope is 3/2 which means rise equals three and run equals two. Rise is Y2-Y1 the run is X2-X1. So if we start at point zero and three and we go rise three, rise three means go up three, one, two, three and we run along two which means the difference in X coordinate is two. This is our second point. What’s the second point? It is X value equals two and Y value equals six. So now that I have these two points I can just draw a line that runs through this points and that’s our graph. To recap, what do we do? We understood that the Y intercept is three which give us one of the coordinates. Once I have one of the coordinates and we have the slope, slope told me the rise and the run. Rise means you go up Y-axis, run means you go to the right on the X-axis. So the rise was three we could go up three and the run was two we could go down two which means this is the second point. So now that I have two points there can only be one line that goes through it that’s our graph. Let’s try one more. In this example, we’re given a different formula. The formula that we’ve been using is y2-y1 equals m(x2-x1) so that’s the way this has been written. So what am I given? Y2 is y, y1 is three. What else do I know? Negative two is m, so the slope is negative two and x1 equals one. Y1 is actually negative three because it’s y2 minus y1. So another way to write this would be y-(-3) = -2(x-1). This is x1, this is y1. So what do I get? Y1 equals negative three, m equals negative two, x1 equals one. Since I knew x1 and y1, this is point A which is X value of one, y coordinate negative three. So that’s the first thing that we’re given, we’re given one of the coordinates. So I’ll plot one of the coordinates, one and negative three. Then we’re given the slope. The slope is negative two or negative over one so rise is negative two run is one. So now that I have one coordinate let’s actually rise negative two which means if rise is negative two I go down to Y-axis two points. So I was at negative three, I went down to negative five and then the run is positive on which means to the right so I’ve got my second point. So now that we’ve got two points I can draw a line through them and that’s the graph for this. Key thing to remember is the two ways you can express a line with this one equation of a line, this is the other equation of a line y=mx+b. As long as we know this we can substitute the values to find one coordinate. If we have one and we know the slope we can calculate the second coordinate and the graph is the line that connects the two extended infinitely in both directions.