Graphing a Linear Equation
An equation that can be written in the form Ax + By = C is called a linear equation
because its graph is a straight line.
Here are some examples:
4x + 2y = 12 
y = 2x + 8 
y = 5 (Here, A
≠ 0.) 
x = 6
(Here, B ≠ 0.) 
We can graph a linear equation on a Cartesian coordinate system by
plotting points that satisfy the equation.
Procedure
To Graph a Linear Equation
Step 1 Make a table of ordered pairs that satisfy the equation.
Step 2 Plot the ordered pairs.
Step 3 Draw a line through the plotted points.
Note:
Since two points determine a line, you can
use any two points that satisfy the equation
to draw the line. Plotting more than two
points will help avoid errors.
Hereâ€™s how to calculate the corresponding
value for y when x = 3.
Equation. Replace x with 3.
Multiply.
Add 12 to both sides.
Divide both sides by 6. 
4x  6y = 24
4(3)  6y = 24
12  6y = 24
6y = 36
y = 6 
Example 1Graph the linear equation 4x  6y = 24.
Solution
Step 1 Make a table of ordered pairs that satisfy the equation.
Select values for x and then use
4x  6y = 24 to calculate the
corresponding values for y.
Step 2 Plot the ordered pairs.
The points are shown on the graph.
Step 3 Draw a line through the plotted points.
Each point on the line represents a solution of the equation 4x  6y = 24.
