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Would x = 5 be an undefined slope?

Answer 1

Avery Alexander

The line described by the equation #x=5# has undefined slope.

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

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

In the case of the line #x=5# choose example points #(5, 0)# and #(5, 1)#.

Then #m = (1 - 0) / (5 - 5) = 1/0# which is undefined.

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Answer 2

Isaiah Anthony

No, ( x = 5 ) represents a vertical line with an undefined slope.

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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.

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