What Is a Linear Equation? (Mathematics Lesson)
What Is a Linear Equation?
A linear equation is an equation that shows a straight line when it is plotted.
Real Examples of Linear Equations
Some examples of linear equations are shown below:
Linear Equations as Equations of Lines
A linear equation will often have two variables, x and y.
Certain values of x and y will make both sides of the equation equal.
x = 1, y = 3 (3 = 2 × 1 + 1)
x = 2, y = 5 (5 = 2 × 2 + 1)
x = 3, y = 7 (7 = 3 × 2 + 1)
These pair of x and y values can be plotted on a graph as Cartesian coordinates (x, y). When they are plotted, they make a line:
Forms of Linear Equations
Linear equations come in many forms.
The main thing that makes an equation linear is that the variables (x and y) do not have any exponents (see Note).
The general form of a linear equation is:
The slope-intercept form of a linear equation is:
m is the slope and c is the y-intercept.
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.
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