What is the slope of #x=6# ?

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Answer 1 · 2016-11-06T08:23:29

The slope of a vertical line is undefined.

Given:

#x=6#

This equation describes a vertical line.

The slope of a line describes how much it rises in proportion 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.

So the slope of the line 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]}