Linear Equations (in Slope-Intercept Form)
(KS3, Year 8)

The Lesson

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.
• m is the slope of the line. It tells you the steepness of the line.
• c is the y-intercept of the line. It tells you the y-coordinate of where the line crosses the y-axis.

A Real Example of a Linear Equation in Slope-Intercept Form

An example of a linear equation in slope-intercept form is given below: If we compare this equation to y = mx + c, we can find the slope and y-intercept.

• The number in front of the x is the slope.
  y = 2x + 1
  The slope is 2. Read more about finding the slope from a linear equation
• The number on its own is the y-intercept.
  y = 2x + 1
  The y-intercept is 1. Read more about finding the y-intercept from a linear equation

Other Forms of Linear Equations

There are other forms of linear equation.

• The general form of a linear equation is:
  
  Read more about the general 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. Read more about the slope-point form of a linear equation

Understanding What a Linear Equation Is...

Let's see what parts a linear equation can have: A linear equation can contain:

• Variables (such as y and x above)
• Constants (such as 1 above)
• Coefficients - a constant in front of a variable (such as 2 above)

...And What It Isn't

Now let's see what a linear equation cannot have. If you see any of these, it isn't a linear equation. The variables in the linear equation (the y and x) cannot contain:

• Exponents - variables can only appear as x and y, not as x² or y³
• Roots - variables cannot appear as √x or ∛y