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What is a vertical line ? Here are several ways to describe a vertical line.

• A line perpendicular to the horizon.
• A line that runs up and down on a page.
• A line on a graph that will not cross the y intercept and does not have a y intercept.

In Geometry a horizontal line is a line that is parallel to the horizon. Here are a couple of other ways to describe a horizontal line.
• A line that is perpendicular to a vertical line.
• On a page, a horizontal line is a straight line that runs from left to right .
• A line that has a slope value of zero.
• A horizontal line has a rise which is zero.
• A line that will not cross the x axis, and does not have a x intercept.
• A horizontal line is parallel to the x axis on a coordinate plane.

Common Core Standard   8.E.E.6  8th Grade Math

### What makes a vertical line and horizontal line different?

A horizontal line has a slope of zero and is written y= c c=the constant
Write the equation for a horizontal line that goes through the point (7,3)
The line crosses the y axis at 3, so the equation is y=3

• vertical line has an undefined slope and the equation is written x=c   c=the constant.

Write the equation for a vertical line passing through (4,-5)
x= 4

Horizontal lines have a slope of zero, and run parallel to the x axis.

Vertical lines have a undefined slope, and run parallel to the y axis.

The equation for a horizontal line equals y=c , and the equation for a vertical line equals x=c.

If a horizontal line crosses a vertical line the two lines would be perpendicular to one another.

### Parallel,Perpendicular,Horizontal, and Vertical Lines

A line that is parallel to a horizontal line has a slope of zero. (rise/run, 0/1).

A line perpendicular to a horizontal line has a slope that is the negative reciprocal of zero (rise/run ,-1/0).

Find the equation of a line parallel to y=5, and passes through the point (5,3)
Remember, two parallel never intersect.

The equation y=5 tells you that the line is a horizontal line, so the second line has a slope of zero so the equation would equal y=3.

Write the equation for a line that is parallel to x=6, and passes through the points (12,-4).

Both lines are vertical lines therefore the equation would equal x=12.

Write the equation for a line that is perpendicular to the line x=5 and passes through the points (6,8).

Remember perpendicular lines intersect and form a 90 degree angle.
The original line is a horizontal line, therefore the equation will be y=8.  Vertical  Line Horizontal Line    The Horizontal line D has a slope equal to 0 and the equation is:

y =  2   ( because this is where the line crosses the y axis)
Write the equation of a vertical passing through (-3,3)

x = - 3  ( because this is where the line crosses the x axis)

The equations and slopes of vertical and horizontal lines  are slightly different than a regular line, and can be described as " Special. "

### Examples of Horizontal lines on a coordinate plane.

Transcript

Hi welcome to MooMooMath. Today we are going to look at special slopes of horizontal and vertical lines. I’m going to review the guidelines of slopes. This first example has a slope that is going up when you look from left to right so it is a positive slope and we always count our slope as rise over run. So in the first example we will rise positive 4 and run positive 3 so the slope is positive 4⁄3.Let’s look at the second example, if you move from left to right notice the line is going downward so it will have a negative slope. When we go to count it we will go down 2 and over 1, 2 so it will have a slope of negative 2 over 2 so it will have a slope of negative 1. Again the slope is negative and going down from left to right. Now let’s look at our two special cases. The first one does not go up or down but is horizontal. So any time you have a horizontal lie you have a slope of 0 why is that? You have a rise of 0 and a run of any value so our slope will just be 0. Let’s look at this last one. The equation for this line is y= positive 2. Whenever you have a horizontal line it is always y = the constant of where line crosses the y axis. In this case it crosses the y axis at 2. Now in the last case you have a vertical line. Now the vertical line does not have a slope, or sometimes they call it an undefined slope. Why is it undefined or no slope? We have a rise of any value but it has a run of 0 what do we know when we divide any value by 0? You can’t do that so that is why the value is undefined. So this crosses the X axis at two so the equation of the line is x equals two and no Y value. Let’s look at a summary of our slopes. So here is our Cartesian coordinate plane to find the slope from a to b we count our rise is 3 and our run is 4 so this line is ¾ our slope of our next line is down one over four so it is negative ¼. The slope of our special lines is: the vertical lines (C) are undefined slope or no slope and the slope of the horizontal line (d) is 0. The equation for line d is negative 2 y because that is where the line crosses the y axis a so it is y= negative 2 the vertical line (C) has an equation of x = negative 3 whenever you have a vertical line it is x equals and a horizontal line is y equals that constant. Hope this was helpful.

## Horizontal Lines

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