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Linear Equations
(KS3, Year 7)
The Lesson
A linear equation is an equation that shows a straight line when it is plotted on a graph.An Example of a Linear Equation
An example of a linear equation is shown below:In this example, there are two variables (x and y). None of the variables have a number written to the right and above it (that is, the highest exponent is 1).
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.Linear Equations as Equations of Lines
The linear equation has two variables: x and y.Pairs of values of x and y will make both sides of the equation equal. In the table below, pairs of values of x and y are chosen in the left hand column. They are substituted into the equation (y = 2x + 1) in the right hand column. Both sides of the equals sign are equal.
x = 1, y = 3 | 3 = 2 × 1 + 1 \(\:\:\:\) = 2 + 1 = 3 ✔ |
x = 2, y = 5 | 5 = 2 × 2 + 1 \(\:\:\:\) = 4 + 1 = 5 ✔ |
x = 3, y = 7 | 7 = 2 × 3 + 1 \(\:\:\:\) = 6 + 1 = 7 ✔ |
Forms of Linear Equations
Linear equations come in many forms.-
The general form of a linear equation is:
Read more about the general form of a linear equation -
The slope-intercept form of a linear equation is:
m is the slope and c is the y-intercept.
Read more about 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 (x_{1}, y_{1}) is a point (in Cartesian coordinates) on the line.
Read more about the slope-point form of a linear equation
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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