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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.

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.

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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=(y2y1)(x2x1).
  • 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=0142=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.

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  • y=23x1
  • y=12x+3

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