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Linear Equations (in SlopeIntercept 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 yintercept of the line. It tells you the ycoordinate of where the line crosses the yaxis.
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.A Real Example of a Linear Equation in SlopeIntercept Form
An example of a linear equation in slopeintercept form is given below:If we compare this equation to y = mx + c, we can find the slope and yintercept.

The number in front of the x is the slope.
y = 2x + 1The slope is 2. Read more about finding the slope from a linear equation

The number on its own is the yintercept.
y = 2x + 1The yintercept is 1. Read more about finding the yintercept 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 slopepoint form of a linear equation is:
m is the slope of the line, and the point (x_{1}, y_{1}) is a point (in Cartesian coordinates) on the line. Read more about the slopepoint 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 x^{2} or y^{3}
 Roots  variables cannot appear as √x or ∛y
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