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The Horizontal and Vertical Line

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Vertical Line

While learning English letters you might have practiced standing and sleeping lines. A horizontal line is a sleeping line. Formally you can define a horizontal line as the line drawn parallel to the x-axis. You can see horizontal line in many other shapes. Ex: triangle, rectangle, etc.

The kitchen slab is the best example of horizontal lines. A straight line is usually represented by the equation y = mx+c, where m is the slope of a line and c is the constant.

Vertical Line

While measuring the height of a person you hold the measuring tape from top to bottom. The line drawn parallel to the tape represents the vertical line. It is a line drawn perpendicular to the x-axis or parallel to the y axis. A real-life example of this is an electric pole. 

The Slope of Horizontal and Vertical Lines

Horizontal line: The slope of a line gives the steepness of a line. It is measured by dividing the values of the y axis by the values of the x-axis. The horizontal line is flat so its slope is equal to zero. It means m = 0, So the above equation of a straight line can be written as y = c. This is the equation of a horizontal line. Where y is the value of y coordinate at any point on a line. C is the point at which a line crosses the y-intercept. 

Vertical line: The values of x coordinates in a vertical line are equal. Here also the slope is equal to zero. So the equation of a vertical line is written as x = c or x = – c. Where x is the value of x coordinate at any point on a line. C is the point at which the line crosses the x-intercept. 

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Horizontal and Vertical Line Tests

Horizontal Line: 

The test helps in finding whether the function is one-to-one or not. The function is said to be one-to-one if there exists a single x value for every y value.  

Ex: Monday you eat an apple, Tuesday an orange, Wednesday papaya, Thursday grapes, Friday lichi, and Saturday a watermelon. This represents the one-to-one function because each day is paired with different fruit. 

If you eat an apple on Monday an apple, Tuesday an orange, Wednesday a papaya, Thursday an apple, Friday lichi, and Saturday a watermelon. Then this is not a function because on Monday and Thursday you are eating an apple.

Vertical line: 

The vertical line test is handy in determining whether the relation is a function or not. As per the definition of a function, every image has got a pre-image. The given relation can be checked by drawing a vertical line. If it intersects at a single point on the graph, then the relation is a function. If the vertical line intersects at more than 1 point then the relation is not a function. 

Ex: Graph of a parabola representing a quadratic equation is a perfect example of a function. Because the vertical line intersects the graph at a single point here. 

Difference Between Horizontal and Vertical Lines

  1. The horizontal line is parallel to the x-axis and perpendicular to the y axis. Whereas vertical lines are parallel to the y axis and perpendicular to the x-axis. 
  2. Horizontal lines are drawn either from left to right or from right to left but vertical lines are drawn from top to bottom or from bottom to top. 
  3. Horizontal line equation is y = c and the vertical line equation is x = c.
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With this ends the horizontal and vertical line topic. For further more curious information log onto the Cuemath website.

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