What is the equation of a line perpendicular to the line #y-2x=5# and goes through (1,2)?

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Answer 1 · 2015-11-14T03:31:52

#y=\frac{-x+5}{2}#

#y=2x+5#

We can see that the slope #m=2#. If you want a line perpendicular to your function, then the slope would be #m'=-1/m=-1/2#.

And so, you want your line to go through #(1,2)#. Using the point-slope form:

#y-y_0=m'(x-x_0)#

#y-2=-0.5(x-1)#

#y-2=-0.5x+0.5#

#y=-0.5x+0.5+2#

#y=-0.5x+2.5#

#y=-1/2x+5/2#

#y=\frac{-x+5}{2}#

The red line is the original function, the blue one is the perpendicular which goes through #(1,2)#.