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What is the slope of #x=6# ?

Answer 1

Ethan Adkins

The slope of a vertical line is undefined.

Given:

#x=6#

A vertical line is described by this equation.

A line's slope indicates how much it rises relative to its run.

Given two distinct points #(x_1, y_1)# and #(x_2, y_2)#, the slope #m# of the line through them is given by the formula:

#m = ("change in " y)/("change in " x) = (y_2-y_1)/(x_2-x_1)#

In our example, consider the two distinct points #(6, 0)# and #(6, 1)#.

Both of these satisfy the equation #x=6#, so lie on the line.

Thus, the line's slope is:

#m = (1 - 0)/(6 - 6) = 1/0#

which is undefined, since division by #0# is (almost) always undefined.

graph{(x+y*0.000001-6)((x-6)^2+y^2-0.006)((x-6)^2+(y-1)^2-0.006)=0 [-0.73, 9.27, -1.94, 3.06]}

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Answer 2

Ethan Adkins

The slope of the line x = 6 is undefined.

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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.