Is the slope of x = 0 is undefined?

Answer 1

Yes, the slope of the line given by the equation #x=0# is undefined.

If a line passes through two points #(x_1, y_1)# and #(x_2, y_2)# then the slope #m# of the line is given by the formula:

#m = (Delta y)/(Delta x) = (y_2 - y_1)/(x_2 - x_1)#

In our case, then line #x=0# passes through #(0, 0)# and #(0, 1)#, so we can (attempt to) calculate its slope as:

#m = (y_2 - y_1)/(x_2 - x_1) = (1 - 0) / (0 - 0) = 1/0#

#1/0# is undefined, so the slope is undefined.

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Answer 2

Abigail Allen

Yes, the slope of the vertical line x = 0 is undefined. This is because a vertical line has a slope that is considered to be "undefined" in mathematics. The reason for this is that the slope formula involves dividing by the change in x, and for a vertical line, there is no change in x (it remains constant), resulting in division by zero, which is undefined in mathematics.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.