Find the equation of the line through the point (6 , -1) and is perpendicular to the y axis.

Let's put the problem in this way: if the line is perpendicular to y-axis, then it is parallel to x-axis.

The slopes of 2 parallel lines are equal:

m1=m2

But the slope of the x-axis is m1=0, so m2=0, also.

Now, let's write the equation of a line which passes through a given point A(6 , -1) and it has a known slope, m2=0:

y - yA = m2(x - xA) 

y - (-1) = 0*(x - 6)

y + 1 = 0

y = -1

The equation of the line which is perpendicular to y-axis is:

y = -1