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Finding the Equation of a Line
(KS3, Year 8)

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We can find the equation of a line. The equation will be a linear equation.

How to Find the Equation of a Line

Finding the equation of a line is easy.

Question

What is the equation of the line shown below? equation of a line example

Step-by-Step:

1

Find the y-intercept of the line. Find where the line crosses the y-axis. The y-intercept is 1 In our example, the y-intercept is 1.

2

Find the slope of the line.

equation of a line step 2

Slope = How far up ÷ How far across

Slope = 4 ÷ 2

Slope = 2

In our example, the slope is 2.
Write the linear equation. The slope-intercept form of a linear equation looks like:
y = slope x + y-intercept

3

Write y = x with space before the x: equation_of_a_line_step_3

4

Write the y-intercept from Step 1 (1) after the x. equation_of_a_line_step_4 Note: The y-intercept is + 1 because it is 1 above the x-axis. It would be −1 if it was 1 below the x-axis.

5

Write the slope from Step 2 (2) before the x. equation_of_a_line_step_5

Answer:

The equation of the line is y = 2x + 1.

Lesson Slides

The slider below shows another real example of how to find the equation of a line.

Slope-Intercept Form of the Equation of a Line

The slope-intercept form of an equation of a line is shown below:linear_equation_slope_intercept_form_mini
  • m is the slope of the line.
  • c is the y-intercept of the line.
Replace m and c with the slope and y-intercept of the line.
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This page was written by Stephen Clarke.

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Worksheet

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