# 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.

## Astep-by-step guide towriting 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 forWriting an Equation from a Graph

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

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

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