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
