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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.
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