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Lesson plan

Write an Equation From a Graph Lesson plan


In this lesson, students will learn how to write a linear equation from a graph. Students will review graphing lines using slope-intercept form. Then, they will apply that knowledge to determine what they should look for when writing the equation. You can expect this lesson with additional practice to take one `45`-minute class period.

Grade 8
Linear Relationships And Functions
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Students will be able to write a linear equation from a graph.


  • Teacher Slideshow
  • Student Resource: Guided Notes
  • Online Practice

How to Teach Writing Equations From a Graph

Warm Up

Give students a copy of the Student Resource sheet. Students should start by reviewing how to graph lines using slope-intercept form. Allow students to work independently before checking with a partner.

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These two graphs are intended to help you check for student misconceptions like:

  • Misidentifying which value represents slope and `y`-intercept in the formula
  • Plotting the `y`-intercept on the `x`-axis
  • Counting the slope as run over rise instead of rise over run
  • Accidentally graphing positive slope when it is negative and vice versa

Making connections

Help students make connections with their prior knowledge and writing equations from a graph. Have students use the examples from the warm up to help them consider the following questions:

  • What is a general formula for the graph of a line? `y = mx + b`
  • What information do you need to write an equation of a line? Slope and `y`-intercept
  • How can you identify the slope and `y`-intercept if you’re only given the graph of a line? Visually look for the `y`-intercept, count the rise over the run

Positive slope

For the first example, the line has a positive slope. Give students a moment to identify the `y`-intercept and slope of the line to help them write their equations.

Students may have the following misconceptions:

  • Identify the `x`-intercept instead of the `y`-intercept
  • Use the wrong sign to represent slope or `y`-intercept
  • Writes the slope as run over rise instead of rise over run
  • Does not simplify the slope
  • Switches the `y`-intercept and slope in the formula and wrote it as `y = bx + m`

Negative slope

Similar to the previous example, give students time to identify the slope and `y`-intercept to try and write their equation.

Some students will write the slope as a positive number, so it will be helpful to ask a student who wrote their slope as negative how they decided that. Some students may say that they recognized the slope was negative because of the direction of the line. Other students may notice that they went up and left (or down and right), so one of the directions was negative and one was positive.

Whole number slope

Allow students time to write the equation from the graph. 

You may notice that students will still write the slope as a fraction even though it’s a whole number. Remind students to simplify when possible when they are writing the equation from a graph.

Different scales on axes

This example may cause some students to hesitate because the scaling is different on the graph. Give students time to work independently or with a partner to try and write the equation of the line from the graph.

It can be helpful to mention to students that in this case, the scales of both axes are the same, so they could still count the slope if they wanted to. Be sure students understand that if the scales are different for the axes, they cannot just count the boxes.

Writing Equations from a Graph Practice

After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of practice problems for writing equations from a graph. Check out the online practice and assign to your students for classwork and/or homework!

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Writing Equations from a Graph Practice
Problem 1 of 8
<LineGraph data-props='{ "options": { "x_min": -1, "y_min": -1, "y_max": 10, "x_max": 10, "cell_size": 20, "x_interval": 1, "y_interval": 1, "x_label": "", "y_label": "", "x_axis_name": "x", "y_axis_name": "y" }, "points": [ { "id": 0, "x": 0, "y": 2,"show_point": true, "highlight_point": true, "highlight_point_color": "black" }, { "id": 1, "x": 2, "y": 3, "show_point": true, "highlight_point": true, "highlight_point_color": "black" }, { "id": 2, "x": 4, "y": 4, "show_point": true, "highlight_point": true, "highlight_point_color": "black" }, { "id": 3, "x": 6, "y": 5, "show_point": true, "highlight_point": true, "highlight_point_color": "black" }, { "id": 4, "x": 8, "y": 6, "show_point": true, "highlight_point": true, "highlight_point_color": "black" }, { "id": 5, "x": -1, "y": 1.5 }, { "id": 6, "x": 10, "y": 7 } ], "line_segments": [ { "first_point_id": 5, "second_point_id": 6, "show_start_arrow": true, "show_end_arrow": true, "highlight_line": "black" } ], "legend_options": {}}'></LineGraph ><p>What is the equation of the line graphed above? <br><highlight data-color="#666" data-style="italic">Write your answer in slope-intercept form using integers and/or simplified fractions.</highlight><p>

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