Graphing Equations by Plotting Points
We can plot a set of points to represent an equation. When such an equation contains both an x variable and a y variable, it is called an equation in two variables. Its graph is called a graph in two variables. Any graph on a two-dimensional plane is a graph in two variables. Suppose we want to graph the equation . We can begin by substituting a value for x into the equation and determining the resulting value of y. Each pair of x- and y-values is an ordered pair that can be plotted. The table below lists values of x from –3 to 3 and the resulting values for y.
How To: Given an equation, graph by plotting points.
- Make a table with one column labeled x, a second column labeled with the equation, and a third column listing the resulting ordered pairs.
- Enter x-values down the first column using positive and negative values. Selecting the x-values in numerical order will make the graphing simpler.
- Select x-values that will yield y-values with little effort, preferably ones that can be calculated mentally.
- Plot the ordered pairs.
- Connect the points if they form a line.
Example 2: Graphing an Equation in Two Variables by Plotting Points
Graph the equation by plotting points.Solution
First, we construct a table similar to the one below. Choose x values and calculate y.
Construct a table and graph the equation by plotting points: .
