now let's say if we have an equation that looks like this 2x + y is equal to 3 how would you write this equation in slope intercept form so right now it's given to us in standard form that is in ax + b y = c format but we need to convert it into slope intercept form that is into y = mx + b in order to convert it into slope intercept form what you need to do is solve for y get y on one side of the equation by itself so for this particular problem all we need to do is move the 2x from the left side to the right side it's positive 2x on the left but when we move it to the right side it's going to become -2X so let's go ahead and do that so this is going to be Y is equal to -2x + 3 the Y variable is still on the left side three is still on the right side all we've done is move 2x from the left side to the right side so now we have the equation in slope intercept form form M which is the slope that's the number in front of X so we're on Part B identify the slope and Y intercept so the slope is -2 b b is the Y intercept that's the constant term in the equation B is equal to 3 so now that we know the slope and the Y intercept we can now draw a graph of the equation which is part C so let's go ahead and do that I'm just going to rewrite it over here I'm going to go up to five on both sides of the x axis and on the y- AIS so the first thing I'm going to do is I'm going to plot the Y intercept the Y intercept is three and that corresponds to the point 03 on the graph so x is 0 Y is 3 and that's going to be right here the slope is -2 so when you think of slope think of Rise overrun a slope of -2 means that we're going to rise two units down and we're going to run one unit to the right so we're going to go down two units one unit over so that will take us to the next point which is 1 one and then we're going to go down to over one and at this point we can draw a line so that's how we can graph a linear equation in slope intercept form now let's work on another practice problem try this one so let's say we have the equation 3x - 4 Y is equal to 12 go ahead and write the equation in slope intercept form identify the slope and Y intercept and then graph the equation so let's begin by taking 3x and let's move it to the other side so we have -4 y on the left side that's equal to -3x + 12 our goal here is to get y by itself we want to solve for y in this equation however in this problem we have a -4 attached to the Y so to get rid of that4 we're going to divide every term by -4 so on left all we have is y is equal to here we have -3 / -4 the two negative signs will cancel into a positive sign so we can write that as positive 34 * X and then 12 / -4 that's -3 so now we have the equation in slope intercept form that is in y = mx plus b format so now let's identify the slope and the Y intercept so the slope is simply the number in front of X in this case it's 3 over 4 B the Y intercept is that number so our B value is -3 so that's how we can identify the slope and Y intercept of the line when it's in slope intercept form now the last thing that we need to do is we need to graph the equation so let's go ahead and do that so now let's begin by plotting the Y intercept so the Y intercept is -3 so we just got to plot -3 on the Y AIS which is here now to find the next point we need to use the slope the slope is 3 over 4 so keep in mind the slope you could think of it as the rise over the run so we have a rise of three a run over four and we can use that to get the next point so starting from the first point our Y intercept we're going to rise three units and then we're going to run four units to the right so that's going to take us to this point here our x intercept which turns out to be 4 or 4 comma 0 so we went up three over four now we can do that again to get another point if we want to but we may need to extend the graph to the right so we're going to go up three and then over four units to the right so once you have the slope you could find an additional Point starting from the first point or any point that you have on a graph so that's how we can graph uh this particular equation so the first thing you want to do is plot the y intercept and then once you have that point use the slope to find the second and even the third point if needed