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# Horizontal and Vertical Lines

By this point, we all know the definitions of vertical and horizontal lines. One moves up and down while the other moves left and right. But there is much more to learn about horizontal and vertical lines, especially when we examine their properties on a plane. Let's take a closer look at these properties:

## Equations of horizontal and vertical lines

Equations of horizontal and vertical lines have only one variable. For example, $x=4$ . This equation shows us that x is always 4, and that the variable y can be any value. Let's see what this looks like on a graph:

As we can see, $x=4$ forms a vertical line. Every ordered pair with 4 as its first coordinate is a possible solution, and this forms a straight line. $\left(4,y\right)$

Now let's take a look at a horizontal line:

$y=\left(-3\right)$

We know that the y coordinate must equal (-3), but we can substitute any value we want for x. What do we get? Take a look:

Any ordered pair that has a -3 for the y coordinate is plotted on this graph: (x,-3).

Just for fun, let's put both of these lines together to find the point at which they intersect:

Finding this intersecting point is easy with a graph -- but we don't necessarily need to go through the trouble of drawing out the coordinates. Instead, we can simply combine both of the known coordinates to get $\left(4,-3\right)$ .

Lines