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 Dependent Variable

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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.

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 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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