Writing an Equation of a Line from a Graph

Equation

Remember the equation of a line is

y = mx + b

where m is slope (rise over run from one point to another)

and b is the y-intercept (where the line crosses the y-axis)

and x and y are variables

Graph

When we look at a graph, we can find the slope (m) and the y-intercept (b)

(We can also find lots and lots of x’s and y’s, but we’ll get to that later)

We find slope by looking at two points on the line. Here, we’re looking at (2, 1) and (4, 4).

We find the rise (how far it is from one y-value to the other—up and down) is 3—because we have to go up three to get from 1 to 4.

We find the run (how far it is from one x-value to the other—left and right) is 2—because we have to go to the right two to get from 2 to 4.

Then our slope is rise over run: 3/2.

We find the y-intercept by looking at where the line crosses the y-axis (the vertical line in the middle of the graph). Here, the line crosses the y-axis at -2. So the y-intercept is -2.

Write the Equation

Now we can write the equation with the information from the graph. We just plug in the slope for m, and the y-intercept for b in the slope-intercept equation y = mx + b.

y = (3/2)x - 2