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How to Graph Vertical and Horizontal Lines


The equation of any vertical line comes in the form

  • where "a" is just a constant.

Notice that this equation doesn't contain any variable y. The absence of y means that it can take any values. Here's an example.

Graph the vertical line x=3.

The equation doesn't have the variable y which implies that it could assume any numerical values for y. In the table of values, you will see that "3" is the repeating value in the column of x while having different values in the column of y.

This is precisely the interpretation of the equation x=3.

table of values whose x coordinates are the same while the y-coordinates are different

So, we can now plot the points in the xy axis to see how it looks. As you can see, it is a vertical line parallel to the y-axis and passing through the point (3,0).


graph of the vertical line x=3 in an xy axis



On the other hand, the equation of any horizontal lines come in the form

  • where "c" is just a constant.

This time around, the equation doesn't have any variable x. The absence of x means that the variable x can take any numerical values while the value of y is being held constant. Here's an example.

Graph the horizontal line y=-2.

Since we have no x-variable in the equation, it is okay to pair the y-coordinate of "-2" with any x-values. When you construct the table of values for this, the y-coordinates will be the same throughout while the x-coordinates will assume different unique values.

Observe, the y-column is populated with the same value of -2.

table of values whose y-coordinates are the same while the x-coordinates are different

Graphing these points in the xy axis, we have a horizontal line parallel to the x-axis and passing through the point (0,-2).


graph of the horizontal line y=-2 in an xy axis



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