Finding The Slope of Horizontal And Vertical Lines [With Solved Examples]
Finding the slope of horizontal and vertical lines is one mathematics problem that can prove to be a challenge if proper understanding isn’t in place.
First and foremost, shall we get the definition of what a line is? A line whether it is vertical or horizontal is the distance between two points.
The extent of the steepness of a line is known as its slope or gradient. How bent or inclined a line is at an angle is the measure of its slope. That being said, lines can take the inclined, horizontal, or even vertical fashion.
There are two chief ways of finding the slope of horizontal and vertical lines. You could take the route of plotting a graph or the route of using the slope formula might just suffice.
Two Ways of How To Find The Slope of Horizontal and Vertical Lines
With that in place, this article would major only on how to find the slope of horizontal and vertical lines.
It is important to note at this point that, horizontal and vertical lines are special types of lines because when written in the form of an equation, they have only a single variable.
At this juncture, it is only relevant we expose what the equation form is:
y = MX + c
Where,
m = slope or gradient
c = intercept on the y-axis
y and x are the variables.
A normal equation for a line has the two variables x and y. An exception to the rule is in the horizontal and vertical lines.
Horizontal lines have just the y variable but no x variable. Whilst the vertical lines have just the x variable but no y variable.
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Equations for the horizontal and vertical lines
For a horizontal line, they have just a y variable since there is no point of contact with the x-axis. Therefore the equation formula is transformed to:
y = c
Where c is the intercept on the y-axis
For a vertical line, they have just an x variable and since there is no point of contact on the y-axis, the equation is, therefore:
x = c
Where c is the intercept on the x-axis.
What is the Slope of horizontal and vertical lines?
Recall that slope of horizontal and vertical lines tell you how inclined that line is. Permit me to add, that slopes show how high or low a line rises or falls.
For a horizontal line, the points move on a straight line from left to right or vice versa. And the slope is therefore zero. The y variable doesn’t change at all. It doesn’t rise or fall.
For a vertical line, the points move on a straight line from top to bottom or vice versa. The slope, therefore, is undefined. There is no y variable in the first place to track whether it is rising or falling.
Generally, horizontal lines have an undefined slope and vertical lines have a slope of 0.
Examples of How To Find The Slope of Horizontal and Vertical Lines
Let’s have examples to cement this lesson.
What is the slope of y = 4
This shows the equation of a vertical line with an intercept of 4 on the y-axis.
Therefore, it has a slope of 0.
What is the slope of x = 5
This shows the equation of a horizontal line with an intercept of 5 on the x-axis.
Therefore, it has an undefined slope.
What is the slope of x = -3
This shows the equation of a horizontal line with an intercept of -3 on the x-axis.
Therefore, it has an undefined slope.
Conclusion
It is of great importance that you bear in mind when faced with questions bordering on the slope of the vertical and horizontal line, that for any horizontal line, the slope would always remain undefined. The same can’t be said for vertical lines. This is because vertical lines always take the slope of zero.
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