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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.

Here’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 1

Graph 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.

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