What is the equation of the line that passes through (3,2) and is perpendicular to the line 2x+y-1=0?

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

We'll put the given equation of the line in
the slope intercept form:

y = mx +
n

y = -2x + 1

Comparing both
equations, we'll get the slope m = -2.

The slope of the
perpendicular line is m1 = 1/2

The equation of the line
that is passing through the point (3,2) and it has the slope m1 = 1/2,
is:

y - 2 = (1/2)*(x-3)

y - 2
= x/2 - 3/2

y = x/2 - 3/2 +
2

y = x/2 +
1/2

The requested equation of the
perpendicular line is y = x/2 + 1/2.