Linear Equations (in General Form)
(KS3, Year 9)

homesitemaplinear equationslinear equations in general form
A linear equation is an equation that represents a line. A linear equation can be written in the form: a x plus b y plus c equals 0 On a graph, a linear equation looks like a line: line on a graph

A Real Example of a Linear Equation in General Form

An example of a linear equation in general form is given below: 4 x plus 2 y plus 8 equals 0 In this example, a = 4, b = 2 and c = 8. We can not directly tell anything about this line from this equation. We can use algebra to convert this equation from general form to slope-intercept form, and then find the slope and y-intercept:

4x + 2y + 8 = 0

2y = −4x − 8

y = −2x − 4

This line has a slope of −2 and a y-intercept of −4.

converting a linear equation in general form to slope-intercept form
finding the slope from a linear equation in general form
finding the y-intercept from a linear equation in general form

Other Forms of Linear Equations

There are other forms of linear equation.

Interactive Widget

You can use this interactive widget to create a graph of your linear equation. Use the buttons to change the values of the linear equation.
Change the Equation
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This page was written by Stephen Clarke.

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