Linear Equations in two Variables

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In this section, we will review linear equations in two variables. These equations are of the form: ax + by = c. A solution to a linear equation in two variables is generally given as an ordered pair (x,y). A solution can be found by picking a number for x and solving for the unknown y-value. We could also reverse this process and choose a value for y and solve for the unknown x-value. For a given linear equation in two variables, there are an infinite number of solutions or ordered pairs. To deal with this, we generally sketch a graph using the Cartesian coordinate plane, which is also called the rectangular coordinate plane. The graph gives us a visual representation of all solutions of the equation. We graph an equation by finding three ordered-pair solutions and plotting the ordered pairs. We then sketch a line through the ordered pairs and place arrows at each end. The arrows indicate that the line continues forever in each direction.
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