How do you find the slope that is perpendicular to the line # y= -1#?

1 Answer
Jun 22, 2016

Answer:

It is undefined.

Explanation:

The slope #m# of a line passing through points #(x_1, y_1)# and #(x_2, y_2)# is given by the formula:

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

The line #y = -1# passes through the points #(0, -1)# and #(1, -1)#. So it has slope:

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

Alternatively, simply note that #y=-1# can be rewritten:

#y = 0x+(-1)#

which is in standard slope intercept form:

#y = mx+b#

with slope #m = 0# and intercept #b=-1#.

#color(white)()#
If a line has non-zero slope #m#, then any line perpendicular to it will have slope #-1/m#.

The line #y=-1# has slope #0# so any line perpendicular to it will have undefined slope. If you try to evaluate #-1/m#, it involves division by #0#, which has undefined result.