Graphing Horizontal and Vertical Lines

If the coefficient of a variable in a linear equation is 0, then that variable is usually omitted from the equation. For example, the equation y = 0 Â· x + 2 is written as y = 2. Because x is multiplied by 0, any value of x can be used as long as y is 2. Because the y-coordinates are all the same, the graph is a horizontal line.

Example 1

Graphing a horizontal line

Graph y = 2. Plot at least four points.

Solution

The following table gives four points that satisfy y = 2, or y = 0 Â· x + 2. Note that it is easy to determine y in this case because y is always 2.

 x -2 -1 0 1 y = 0 Â· x + 2 2 2 2 2

The horizontal line through these points is shown in the figure below.

If the coefficient of y is 0 in a linear equation, then the graph is a vertical line.

Example 2

Graphing a vertical line

Graph x = 4. Plot at least four points.

Solution

We can think of the equation x = 4 as x = 4 + 0 Â· y. Because y is multiplied by 0, the equation is satisfied by any ordered pair with an x-coordinate of 4.

 x = 4 + 0 Â· y 4 4 4 4 y -2 -1 0 1

The vertical line through these points is shown in the figure below.