Graphing Linear Equations

Linear equation graphs are always a straight line. And you just need two points to draw a straight line (try it out!), which is the key to drawing the graphs.

Try using our step by step linear equation graphing calculator below! You can also find the linear equation of a given graph using our step by step guide by scrolling down.

If you have two points or one point and a slope, you'll need to first find the slope-intercept form of your line. Use this calculator to do that first!


Graphing a Linear Equation

There are four easy steps to graphing a linear equation:

  1. Slope-intercept form: The first step to graphing a linear equation is getting our equation in slope-intercept form,
    where and represent numbers. Enter in some numbers for and .
  2. Plot the y-intercept: Now, remember, we need two points to draw a line. The easiest point to get is the y-intercept, where . All we need to do is plug-in for in our equation:
    So, the first point we can plot is :
  3. Plot another point: We need another point, and we can find it by plugging in any other number in for . We're going to pick , so all we need to do is plug-in for in our equation:
    So, the second point we can plot is :
  4. Connect the lines: All that's left to do now is connect the dots 👏🏿👏🏾👏🏼!

Graph to Linear Equation

There are five easy steps to getting the linear equation from a graph:

  1. Find two points: We need two points to figure out our equation. So, we should look for two points that have whole numbers as and coordinates.
    Let's say this is our graph:
    We're going to pick the two blue points, which are and .
  2. Get the slope: Next, we need to use our two points to get the slope of the line. Let's remember how to get the slope...

    Slope Formula

    Let's say we have two points: Point 1 with coordinates and Point 2 with coordinates . The slope is given by the change in by the change in :
    So, with our two points, our slope is:
  3. Slope-intercept form: Now, we can plug our slope into slope-intercept form, which is
    where is the slope. Plugging in our slope of 3, we get
  4. y-intercept: Finally, we need to get our value for . We can do this, by plugging in one of original points. We're going to choose the first point: Plugging in, we get this:
    If we solve this equation, we get:
  5. Final equation: Now, we can plug our value in to get our equation: