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Linear Equations

A linear equation is an equation with two variables, usually x and y. The solution to a linear equation is an ordered pair (x, y) that makes the equation true.

The graph of a linear equation is the set of all ordered pairs that are solutions of the equation.

When the solutions are graphed, the points form a line, which is why these are called linear equations.

Determining a Solution

To determine if an ordered pair is a solution to a linear equation, you will substitute the values for x and y. After substituting, you will simplify each side of the equation to determine if one side is equal to the other.

Example #1

Let's learn how to determine if an ordered pair is a solution to a given linear equation.

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Graphing Linear Equations

The first method you will learn to graph linear equations is using an x-y table. This method will always work for any type of equation or function in two variables. Using this table, you will substitute values of x to evaluate for values of y and create ordered pairs.

When constructing your x-y table, you will want at least three points for accuracy of your graph. The more points you plot, the more accurate your line.

Graph a Linear Equation Using an X-Y Table Example #2

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Example #3

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Example #4

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