What is the equation of the line perpendicular to #y=9/10x # that passes through # (-1,5) #?

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Answer 1 · 2016-01-04T16:48:01

#y=-10/9x+35/9#.

A straight line graph of form #y=mx+c# has gradient #m# and y-intercept #c#.

Perpendicular lines have gradients whose product is #-1#.

So the gradient of the given line is #9/10# and so a line perpendicular to this line would have gradient #-10/9#.

We may now substitute the point #(x,y)=(-1,5)# into the general equation of the required line to solve :

#y=mx+c#

#therefore 5=(-10)/9(-1)+c#

#therefore c=35/9#.

Thus the required line has equation #y=-10/9x+35/9#.