How to Write an Equation from a Graph?
We can use the information presented in a graph to write an equation. In this step-by-step guide, you will learn more about writing an equation from a graph.

A linear equation can be written in various forms such as the standard form, the slope-intercept form, and the point-slope form.
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A step-by-step guide to writing an equation from a graph
There are several forms that the equation of a line can take. They may look different, but they all describe one line – one line can be described by many equations. However, all (linear) equations that describe a particular line are equivalent.
The first of the forms for a linear equation is the slope-intercept form. Equations in slope-intercept form look like this:
y=mx+b
where:
m: the slope of the line
b: the y-intercept of the line or the y-coordinate of the point at which the line crosses the y-axis.
We can use the information presented in a diagram to write an equation in the form of a slope intercept. Follow the steps given below to write an equation from a graph:
- Step 1: Choose two points on the graph, (x1,y1) and (x2,y2), to find the slope. The formula of the slope is: m=(y2−y1)(x2−x1).
- Step 2: Read the y-intercept from the graph. That is the point at which the line cuts the y-axis.
- Step 3: Use slope (m) and y-intercept (b) values to write an equation in slope-intercept form.
Writing an Equation from a Graph – Example 1:
Write an equation of the following line in slope-intercept form.

First, select two points on the line, for example, (2,1) and (4,0). Use these points to calculate the slope: m=0−14−2=−12.
Next, find the y-intercept: (0,2). Thus, b=2.
Therefore, the equation for this line is y=−12x+2.
Exercises for Writing an Equation from a Graph
Write an equation of each line in slope-intercept form.



- y=23x−1
- y=12x+3
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