How to Solve Slope-Intercept Form

By Chad Stetson
You can easily change graphed lines into linear equations.

The slope-intercept form is the easiest way to represent linear equations. It allows you to know the slope of the line and the y-intercept with a simple glance. The formula for a line in slope-intercept form is y = mx + b, where "x" and "y" are coordinates on a graph, "m" is the slop and "b" is the y-intercept. By viewing a graph of a line, you can easily create an equation for that line by translating the graph using the slope-intercept form.

Determine the slope of the given line. To do this, you must know the exact coordinates of any two points of a line. You can quickly calculate the slope by using the formula, (yB - yA )/(xB - xA ), where A and B are two separate points on the line. For example, if point A is (6,4) and point B is (3,1), the formula would be (1 - 4) / (3 - 6), which simplifies to -3 / -3, which simplifies further to 1. The m value in this example is therefore 1.

Find the y-intercept of the line. Most lines have one y-intercept, although some have none. The y-intercept is the point where the line crosses over the y-axis. It is therefore the coordinate where x = 0. For example, if the line crosses over the vertical axis at the point (0, 4), the y-intercept is therefore y = 4, which means that the value of b is also 4.

Build the equation. Once you know the slope and the y-intercept, you now have all the information you need to construct the equation in the slope-intercept form. Remember, the slope-intercept formula is y = mx + b. Plug in your slope where the "m" value is, and plug in your y-intercept where the "b" is. This is the equation of the line in slope-intercept form. Borrowing from the two previous steps, the example line would be y = 1x + 4, which simplifies to y = x + 4.


The slope-intercept formula can also serve to change an equation into a graph. Simply follow the reverse instructions to do this: Plot the y-intercept as one point, and use the m value to draw a second point on your graph. Connect the two points to create the line.