What is the slope of the line perpendicular to #y=4/17x+7 #?

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Answer 1 · 2016-02-01T03:50:04

slope#=-17/4#

Recall that when a line is perpendicular to another line, its slope is the negative reciprocal of the slope of the other line.

To find the negative reciprocal:

#1.# Flip the positions of the numerator and denominator around
#2.# Multiply the whole fraction by #-1#.

Note that you can also multiply the whole fraction by #-1# first before flipping the positions of the numerator and denominator; either way works.

Thus:

#4/17color(red)(rArr)17/4color(red)(rArr)-1*17/4color(red)(rArr)-17/4#

OR

#4/17color(red)(rArr)-1*4/17color(red)(rArr)-4/17color(red)(rArr)-17/4#

#:.#, the slope of the line perpendicular to #y=4/17x+7# is #-17/4#.