How to Write 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.

Related Topics

• How to Write Linear Equations?

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, \((x_1, y_1)\) and \((x_2, y_2)\), to find the slope. The formula of the slope is: \(m=\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}\).
• 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: \(m=\frac{0-1}{4-2}=-\frac{1}{2}\).

Next, find the \(y\)-intercept: \((0, 2)\). Thus, \(b=2\).

Therefore, the equation for this line is \(y= -\frac{1}{2}x + 2\).

Exercises for Writing an Equation from a Graph

Write an equation of each line in slope-intercept form.

• \(\color{blue}{y=\frac{2}{3}x-1}\)
• \(\color{blue}{y=\frac{1}{2}x+3}\)