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 Depdendent Variable

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 Dependent Variable

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# Graphing Horizontal Lines

A linear equation in two variables is an equation that can be written in the form Ax + By = C, where A, B, and C are real numbers and A and B are not both 0.

If either A or B is 0, the equation can be written with only one variable.

For example, the equation y = -2 is a linear equation since it can be written as 0x + 1y = -2.

Here, A is 0, B is 1, and C is -2.

Now we will graph the equation y = -2.

Example 1

Graph y = -2.

Solution

Step 1 Make a table of ordered pairs that satisfy the equation.

Each ordered pair (x, y) that satisfies the equation y = -2 has y-coordinate -2. So, in the table, y is always -2.

The variable x does not appear in the equation y = -2. So we can let x be any real number; but y is always -2.

 x y -5 -2 -3 -2 0 -2 3 -2

Step 2 Plot the ordered pairs.

The points are plotted.

Step 3 Draw a line through the plotted points.

Since the y-value of each ordered pair is -2, the graph is a horizontal line two units below the x-axis.

Every point on this line represents a solution of y = -2.

Definition â€” Graph of a Horizontal Line y = k
 The graph of an equation of the form y = k is a horizontal line through the point (0, k), where k is a constant.