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

The Lesson

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.

Read more about converting a linear equation in general form to slope-intercept form
Read more about finding the slope from a linear equation in general form
Read more about 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 a linear equation in the slope-intercept form. Use the buttons to change the values of the linear equation.
Change the Equation
y
x
y-intercept
Help Us To Improve Mathematics Monster

  • Do you disagree with something on this page?
  • Did you spot a typo?
Please tell us using this form

See Also

What is a linear equation? Converting a linear equation from general from to slope-intercept form Finding the slope from a linear equation in general form Finding the y-intercept from a linear equation in slope-point form