"Linear" equations are equations with just a plain old variable like "x", rather than something more complicated like x2 or x/y or square roots or such.  Linear equations are the simplest equations that you'll deal with. You've probably already solved linear equations; you just didn't know it.

Solving equations works in much the same way, but now you have to figure out what goes into the x.
Recall the "nicest" equations to solve are linear equations, since we only need to use arithmetic to isolate the desired variable.

Linear equations can always be written in the form:

When we graph such an equation, we can see why they are called "linear."  That is, the graph is a "straight line."

A linear equation is shaped like any other equation. It is two expressions set equal to each other. A linear equation is special because:

1. It has one or two variables.

2. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction.

3. When you find pairs of values that make the linear equation true and plot those pairs on a coordinate grid, all of the points for any one equation lie on the same line. Linear equations graph as lines.
When the equation describes a relationship between two variables in which the value of one of the variables depends on the value of the other variable, x is the independent variable and y depends on it. We call y the dependent variable. If the variables have other names, yet do have a dependent relationship, the independent variable is plotted along the horizontal axis. Most linear equations are functions (that is, for every value of x, there is one value of y). When you assign a value to the independent variable, x, you can compute the value of the dependent variable, y. You can then plot the points named by each (x,y) pair on a coordinate grid. The real importance of emphasizing graphing linear equations with your students, is that they should already know that two points define a line, so finding many pairs of values that satisfy a linear equation is easy: Find two pairs of values and draw a line through the points they describe. All other points on the line will provide values for x and y that satisfy the equation.