How do you find the slope of a line perpendicular to a slope 0?

Question

Ethan Adkins · Accepted Answer

The slope of a line perpendicular to a line with a slope of #0# is undefined. The perpendicular line is a vertical line.

A line with a slope of #0# is a horizontal line. A vertical line would be perpendicular to the horizontal line, but the slope of a vertical line is undefined.

For example:

The following points will result in a vertical line because the x-coordinates are the same.

#(2,3)# and #(2,4)#

#m=(4-3)/(2-2)#

#m=1/0#, which is undefined.

The points represent a vertical line with an undefined slope.

Nathan Axel · Answer

It will of the type #x=k#.

This appears to be a bit complicated as normally we say that if slope of a line is #m#, slope of line perpendicular to it is #-1/m#, which means just take the reciprocal and change the sign. For example if slope of a line is #3/7#, line perpendicular to it will have a slope of #-7/3#. And if slope of a line is #-2#, slope of line perpendicular to it will be #1/2#. What do we do if we have to find the slope of a line perpendicular to a line of slope #0#? The problem is #1/0# is not defined. Way out is even simpler. As equation of a line whose slope is #0# is of the type #y=k_1# (here #k_1# a constant is #y#-intercept - aline parallel to #x#-axis), equation of line perpendicular to it will be #x=k#, where #k# is another constant. Note #k# is #x#-intercept of the line #x=k# and this line is vertical i.e. parallel to #y#-axis.

Julia Adams · Answer

You cannot find the slope.
You can only say that it will be a vertical line and the slope is undefined.

A line with a slope of #0# is a horizontal line. A vertical line is one that is perpendicular to a horizontal line. On the other hand, a vertical line's slope is arbitrary. As a result, it is impossible to determine the slope; all you can predict is that it will be a vertical line with an unknown slope. This is because for any change in #y# values, there is no change in the #x# values. Slope = #(Delta y)/(Delta x) = y/0#

Savannah Anderson · Answer

undefined The slope of a line perpendicular to a line with slope 0 is undefined.