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The Rectangular Coordinate System
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Graphs of Equations

The following are the steps in graphing an equation in the variables x and y on a coordinate plane:
1. Tabulate values of x and y that satisfy the equation.
2. Plot the points that correspond to the ordered pairs (x,  y) obtained in step 1.
3. Draw the line or curve passing through the points.

Example

Graph the equation y=−2x+3.



Solution

First, tabulate the values of x and y that satisfy the given equation. You may assign any real number to x such as –2, –1, 0, 1, 2, and 3. Then, for each value assigned to x, compute for the corresponding value of y.

If x=−2, then
y=−2(−2)+3      =4+3      =7.

If x=−1, then
y=−2(−1)+3      =2+3      =5.
If x=0, then
y=−2(0)+3      =0+3      =3.

If x=1, then
y=−2(1)+3      =−2+3      =1.
If x=2, then
y=−2(2)+3      =−4+3      =−1.

If x=3, then
y=−2(3)+3      =−6+3      =−3.

Tabulating the obtained information gives you the following values:

x −2 −1 0
y 7 5 3

x 1 2 3
y 1 −1 −3

Then, plot the points that correspond to the ordered pairs (x,  y). Plot (−2,  7), (−1,  5), (0,  3), (1,  1), (2,  −1), and (3, −3). Next, connect the points. The plotted points form a line. Label the line with the equation.

The figure below shows the graph of the line.