What is the slope of the line perpendicular to y=16/7x-11y=167x11?

2 Answers
Jul 18, 2016

-7/16716

Explanation:

Recall that the slope mm of a straight line is related to the angle thetaθ that it makes with the XX axis by

m = tan thetam=tanθ

Two mutually perpendicular lines obey theta_2 = theta_1 + pi/2θ2=θ1+π2 so that

m_1 m_2 = tan theta_1 tan theta_2 = tan theta_1 tan (theta_1 + pi/2) = tan theta_1 (- cot theta_1) = -1m1m2=tanθ1tanθ2=tanθ1tan(θ1+π2)=tanθ1(cotθ1)=1

Jul 18, 2016

-7/16716

Explanation:

Consider the standard equation form y=mx+cy=mx+c where mm is the gradient.

Any line perpendicular to this has the gradient of -1/m1m

So for y=16/7x-11y=167x11 the gradient of a line perpendicular to this is

-7/16716