One of the easiest ways to determine the linear equation of a graphed line is to use the slope-intercept formula. The slope-formula is y = mx + b, where x and y are coordinates of a point on a line, b is the y-intercept and m is the slope. The first step to solving the slope intercept formula is to determine the slope. In order to find the slope, you need to know the x and y values for two coordinates on the line.
Set up the slope equation. The slope is simply the ratio between the change in y over the change of x. This means that to determine the slope, you need an equation that allows you to find this ratio. The easiest equation to use is m = (y2 - y1) / (x2 -x1). This equation determines the ratio and is also easy to remember.
Plug the values into the slope equation. You can use any two points on the line. Each point will have an x value and a y values. Use these values in your slope equation. For example, using (4,3) and (2,2), you would place them in the equation as follows -- m = (2-3) / (2-4).
Simplify the equation and solve for m to determine the slope. Use basic addition and subtraction to simplify the ratio. More often than not, your ratio will end up as a fraction. Once you have simplified the equation, you now know the value for the slope between two coordinates. In the example given, (2-3) / (2-4) simplifies to -1 / -2, which simplifies further to 1/2.