now let's say if we have an equation that looks like this two x plus y is equal to three how would you write this equation in slope intercept form so right now it's given to us in standard form that is an ax plus b y equals c format but we need to convert it into slope intercept form that is into y equals m x plus 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 a negative 2x so let's go ahead and do that so this is going to be y is equal to negative 2x plus 3. the y variable is still on the left side 3 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 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 negative two b b is the y intercept that's the constant term in the equation b is equal to three 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 gonna go up to five on both sides of the x-axis and on the y-axis so the first thing i'm going to do is i'm going to plot the y-intercept the y-intercept is 3 and that corresponds to the point 0 3 on a graph so x is zero y is three and that's going to be right here the slope is negative two so when you think of slope think of rise over run a slope of negative two 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 one one and then we're going to go down two 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 minus 4y 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 negative 4y on the left side that's equal to negative 3x plus 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 negative 4 attached to the y so to get rid of that negative 4 we're going to divide every term by negative four so on the left all we have is y is equal to here we have negative three divided by negative four the two negative signs will cancel to a positive sign so we can write that as positive 3 over 4 times x and then 12 divided by negative 4 that's negative 3. so now we have the equation in slope-intercept form that is in y equals 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 three over four b the y intercept is that number so our b value is negative three 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 negative three so we just got to plot negative three on the y axis which is here now to find the next point we need to use the slope the slope is three over four 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 gonna rise three units and then we're gonna run four units to the right so that's gonna take us to this point here our x-intercept which turns out to be four or four comma zero 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 3 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 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