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What are Horizontal Lines? - Definition & Equations

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  • 0:01 What Is a Horizontal Line?
  • 0:07 Examples
  • 1:37 Calculating the Slope
  • 3:26 Equations & Graphing
  • 4:38 Lesson Summary
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Lesson Transcript
Instructor: Betty Bundly

Betty has a master's degree in mathematics and 10 years experience teaching college mathematics.

In this lesson, we will learn about horizontal lines. What properties are unique to horizontal lines? How do you recognize the graph or equation of a horizontal line? These questions will be investigated here.

What Is A Horizontal Line?

A horizontal line is a line which has zero slope value. All points on a horizontal line have the same y value.

Examples

Look at a wall, and look down to where that wall meets the floor. That intersection is a horizontal line. Other examples of horizontal lines we may see every day are the following: the line separating the sky from the land across a clear plain or the line separating the sky from the water at the beach.

Horizon over water
Horizon

Horizon on a plain
Plain

In fact, the word horizontal is derived from the word horizon, the line where the sky meets water. What does your line of motion look like if you move from one point to another without going up or down?

If you are on the second floor, represented by y=2, and you take 5 steps to the left without going up or down any stairs, you are still on the second floor. Your vertical position has not changed. Notice that from left to right, the line does not rise or fall.

Graph of Horizontal Line
Graph of y=2

If you are in the basement, represented by y=-1 and you take 4 steps to the right (again, assuming you have not gone up or down any stairs), you are still in the basement. Again, note that from left to right, the line does not rise or fall.

Graph of Horizontal Line
Graph of x=-1

A line drawn through your two positions in these scenarios would be a horizontal line.

It doesn't matter where you start. You could be walking across the tenth floor of a high-rise. It also doesn't matter how much you may have moved from left to right or from right to left (you cannot have zero movement). If the ending position is at the same height as the beginning position, a line drawn through the two points will be horizontal.

Another way to think of a horizontal line is one that has the same height at all points on the line.

Calculating the Slope

A horizontal line is also recognized as a line that has zero slope. Slope, labeled with the variable m, is defined as rise/run or (change in y value)/(change in x value).

m = rise/run

m= (change in y value)/(change in x value)

In this equation, the rise (change in y value) represents a vertical movement and the run (change in x) value represents a horizontal movement. Since there is no change in vertical motion on a horizontal line, as is described in the graphs above, the numerator of these fractions is zero. This makes the slope of a horizontal line equal to zero.

m= 0/run = 0/(change in x value) = 0

Returning to the 2nd floor scenario, the points on the graph from beginning position to ending position are represented as (6,2) and (1,2), which are (x,y) ordered pairs. To use these coordinate points to calculate the slope, we would use the formula:

slope formula

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