Point-Slope Form Calculator
Write a line's equation in point-slope form from a point and a slope, or from two points.
Also gives slope-intercept form, standard form, and intercepts.
Point-slope form is the quickest way to write the equation of a line when you know one point on it and the slope. It reads y minus y1 equals m times the quantity x minus x1, where (x1, y1) is the point and m is the slope. The appeal is that you can write it down the instant you have those two pieces, without solving for anything first.
It helps to see why it works. Slope is rise over run between any two points on the line, so for a general point (x, y) and your known point (x1, y1), the slope m equals (y minus y1) over (x minus x1). Multiply both sides by (x minus x1) and you have point-slope form. That is the whole derivation, which is why teachers reach for it so often.
If you only have two points, you are not stuck. Find the slope first as the change in y over the change in x, then drop either point into the formula. This calculator does that for you: enter the slope if you know it, or leave it blank and give a second point, and it works out the rest. From there it also converts to the two other common forms. Slope-intercept form, y equals mx plus b, is best for graphing because b is where the line crosses the y-axis. Standard form, Ax plus By equals C, is handier for systems of equations. One edge case worth knowing: a vertical line has an undefined slope and cannot be written in point-slope form at all, so it is just x equals a constant.