What is the equation of the line perpendicular to y = that passes through the point (–2, 4)?

We're looking for a line perpendicular to the line y = x/6

(edit: I accidently calculated a parallel line to x/6.)

Every line has the equation y = ax+b. where a is the slope and b is the y-intercept

Therefore the slope of the line y = x/6 is 1/6

Let's say line A and B are perpendicular,

then slope A = -1/(slope B)

Therefore the slope of a perpendicular line to y = x/6 is -1/1/6 = -6

All perpendicular lines to y = x/6 therefore have the equation

y = -6x+b

Let's see which line passes through (-2,4) by filling in x = -2 and y = 4

4 = -6*-2+b

4 = 12+b

b = -8

Hence the line you're looking for is

y = -6x-8

Reinout 

Thankyou alot, saving me a lot of saneness! Kudos my friend. 

I changed my answer because I made a mistake swapping perpendicular and parallel.

Thank you Alan for making me aware of that .