Write the equation of the line that passes through (1;2) and is perpendicular to y = 6x - 2

If the 2  lines are perpendicular, then the product of the
values of their slopes is -1.

Since the equation is put in
the standard form, y = mx + n, we'll find it's slope:

y =
6x - 2, so the slope is m1 = 6

That means that the second
slope is:

m1*m2 = -1

m2 =
-1/m1

m2 = -1/6

Now, we'll
write the equation of a line that passe through a given point and it has a slope, whose
value is known.

y - y1 = m2*(x -
x1)

The coordinates x1 and y1
are:

y - 2 = m2*(x - 1) and m2 =
-1/6

y - 2 = -(x-1)/6

We'll
add 2 both sides:

y = -x/6 + 1/6 +
2

The equation of the line that passe through the point
(1,2) and it's perpendicular to the line y = 6x-2
is:

y = -x/6 +
13/2