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

A linear equation is an equation that represents a line. A linear equation can be written in the form: On a graph, a linear equation looks like a line:

• y and x are the Cartesian coordinates of points on the line.
• a, b and c are constants. They have no meaning.

A Real Example of a Linear Equation in General Form

An example of a linear equation in general form is given below: 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: 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.

• The slope-intercept form of a linear equation is: m is the slope and c is the y-intercept.
  
  the slope-intercept form of a linear equation
• The slope-point form of a linear equation is:
  
  m is the slope of the line, and the point (x₁, y₁) is a point (in Cartesian coordinates) on the line.
  
  the slope-point form of a linear equation

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