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.
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.
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.