Through (4,-4); perpendicular to 6y=x-12

y = mx + b

m = slope and b = y-intercept

We can arrange 6y = x - 12 in the form of y = mx + b

6y = x - 12

y = 1/6 (x) - 2

Slope of y = 1/6 (x) - 2 is 1/6. Taking the negative reciprocal of the slope we get the slope for the perpendicular line.

Negative reciprocal of 1/6 is - 6.

The equation for the perpendicular line is

y = - 6x + b

To find b we can plug in the x and y values of (4,-4) into it since it passes through those coordinates

-4 = - 6 (4) + b

b = - 4 + 6 (4)

b = - 4 + 24

b = 20

So the equation for the perpendicular line is y = - 6x + 20