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.

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