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Math Lesson 14.2.3 - What is the Gradient of a Horizontal and a Vertical Line?
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Welcome to our Math lesson on What is the Gradient of a Horizontal and a Vertical Line? , this is the third lesson of our suite of math lessons covering the topic of Slopes and Gradients, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
What is the Gradient of a Horizontal and a Vertical Line?
If a line is horizontal, this means there is no change in the vertical coordinate for whatever change in the horizontal coordinate. In symbols, we have Δy = 0 for all values of Δx ≠ 0. From the formula of gradient, we therefore obtain
To confirm the above result, look at the figure below where the line y = 2 is shown.
Substituting the coordinates of points A and B in the gradient's formula yields
= 2 - 2/3 - (-1)
= 0/3 + 1
= 0/4
= 0
On the other hand, the gradient of vertical lines is considered as equal to infinity, because there is no change in the x-coordinate (Δx = 0) for whatever change in the y-coordinate (Δy ≠ 0). In mathematics, a number divided by zero is undetermined, but if we think of it as a non-zero number divided by a very small number, getting closer to zero, the value of the fraction obtained approaches infinity. In symbols, we have
To confirm the above result, look at the figure below where the line x = 3 is shown.
The two points, A(3, 1) and B(3, 3) belong to this graph, so they are suitable for the calculation of the gradient. Thus, we write
= 2/0
= ∞
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