Trig
posted by ali on .
How do you find an equation of a line perpendicular to y=x at the point (5,5) in standard form?

put the original equation in the form
y = m x + b
in this case
y = 1 x + 0
so m, the original slope, = 1
Now m' = 1/m
so our new slope = 1/1 = 1
so our new function looks like
y = 1 x + b
we need b
use the point
5 = 5 + b
b = 10
so
y = x + 10 
The slope of y = x is 1, so the slope of a perpendicular line must be 1. (This is becasue the product of the slopes must be 1).
The equation can therefore be written
(y5)/(x5) = 1
y5 = x +5
y = x +10