In Example 3, what is the solution if x = −3?

Data from Example 3

Graph the equation 2x − y − 4 = 0.

We first need to find several pairs of numbers (x, y) that are solutions to the equation, meaning they make the equation true when x and y are substituted in. If we first solve for y to get y = 2x − 4, the solutions are easier to find. We can substitute any number in for x and then find the corresponding value of y that makes the equation true. The resulting pair of numbers (x, y) is a solution to the equation, and when plotted, is one point on the graph. The table feature on a calculator can be used to find many solutions quickly, as shown in Fig. 5.2. All these pairs of values satisfy the original equation, meaning they make it true. When these points are plotted together, they form the graph of the equation as shown in Fig. 5.3. Note that the graph is a straight line. In general, all linear equations in two unknowns have graphs that are straight lines.

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