How to Graph Point-Slope Form in 3 Steps

Point-slope form is the easiest form to graph, because it hands you a point and a slope directly. You don’t have to convert anything first. Here’s the three-step method, with graphs so you can see each one.

What You Read Off the Equation

Look at y − y₁ = m(x − x₁). The numbers inside give you a point (x₁, y₁) and the coefficient m is the slope. That’s literally everything you need to draw the line.

Step 1: Plot the Point

Take (x₁, y₁) from the equation and mark it on the grid. For y − 3 = 2(x − 1), the point is (1, 3). Remember the sign rule: y − (−2) means the point’s y-value is −2, not 2.

Step 2: Use the Slope to Find a Second Point

Read the slope as rise over run. A slope of 2 is 2/1, so from your point you go up 2 and right 1. That lands you on a second point. If the slope is a fraction like 3/4, go up 3 and right 4.

Step 3: Draw the Line

Draw a straight line through both points and extend it across the grid. You’re done. Here are three examples, each graphed straight from its point-slope equation.

Special Cases

Two slopes behave differently. A slope of 0 gives a flat horizontal line through the point, like y = 3. An undefined slope can’t appear in point-slope form at all, because the line is vertical, so you write it as x = a constant instead.

Check It Instantly

Use the calculator at the top of this page: type your point and slope and the line is drawn for you. To review the algebra, see how to find point-slope form or work through more examples.