Hello!
To find the line perpendicular to y = 6x + 5, you need to find -1/m. -1/m will give you the slope of the perpendicular line. After finding the slope, you need to substitute (3, 2) into the perpendicular without the y-intercept and solve for the y-intercept then.
In the given line, the slope is 6, or m = 6.
-1/m = -1/6
y = -1/6x + b
Now, we need to find the y-intercept.
2 = -1/6(3) + b
2 = -3/6 + b
2 = -1/2 + b (add -1/2 to both sides)
b = 5/2
Therefore, the equation of the line perpendicular to y = 6x + 5 is y = -1/6x + 5/2.