y = -6x + 1....the slope here is -6. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal, flip the original slope and change the sign. So we have a slope of -6 or -6/1.....flip it and it becomes -1/6.....change the sign and it becomes 1/6. So ur perpendicular line will have a slope of 1/6.
y = mx + b
slope(m) = 1/6
(-4,-6)....x = -4 and y = -6
now sub and find b, the y int
-6 = 1/6(-4) + b
-6 = -2/3 + b
-6 + 2/3 = b
-18/3 + 2/3 = b
-16/3 = b
so ur perpendicular equation is : y = 1/6x - 16/3