Question

Through (3,2);perpendicular to 2x+y=1

Answer 1

Get that equation in slope-intercept form first, then take the slope you have, flip it and change the sign. Keep the same y-intercept and that's your equation

Answer 2

\[
2x + y = 1 \\
y = -2x + 1 \\
\]Slope = -2.
Slope of perpendicular line is 1/2.
y = mx + b
y = 1/2x + b.
It passes through the point (3,2). When x = 3, y = 2:
2 = 1/2 * 3 + b
b = 2 - 3/2 = 1/2

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