Slope-Intercept Form

Slope-intercept form is a standard term in upper level mathematics classes. It is a way of organizing an equation to make it easy to graph as a line on a coordinate-plane. Putting an equation in slope-intercept form is the easiest way to graph it, even though there are other ways.

Slope-intercept form is written as y=mx+b, where y and x are variables, m is slope, and b is the y-intercept.

Getting an equation in slope-intercept form, can be very easy. There really only one or two major steps, depending on the equation, but those two major steps involve smaller steps. We are going to start by getting y by itself. In the equation 2x+3y=4x+12, the first step is moving the x variable to leave the y by itself. To do that, we are going to subtract 2x from both sides, because the opposite operation of addition is subtraction.

2x+3y=4x+12
2x+3y-2x=4x+12-2x
3y=4x+12-2x

Now, because there are two x variable on the right side, we are going to combine like terms, by subtracting the 2x from the 4x.

3y=4x-2x+12
3y=2x+12

The next step is getting rid of the 3 in front of the y variable. Because y is being multiplied by 3, we are going to do the opposite operation, division, to both sides to get rid of that 3.

3y/3=(2x+12)/3
y=2/3x+4

Now our equation is in slope-intercept form! From here we can easily identify the parts of the equation. We know that y=mx+b where m is slope and b is the y-intercept. In our equation, 2/3 is the slope and 4 is the y-intercept. We can use use this information to easily graph our equation on a coordinate-plane. Good luck and happy graphing!