$\begin {array} {1 1} (A)\;x-y=5 & \quad (B)\;x+y=5 \\ (C)\;x+y=1 & \quad (D)\;x-y=1 \end {array}$

- If the slope of a line is $m$ then the slope of the line perpendicular to this is $ - \large\frac{1}{m}$.
- Equation of a line passing through $(x_1, y_1) $ and slope $m$ is $y-y_1 = m (x-x_1)$.

Step 1 :

Slope of the line perpendicular to $x=y$ is $m=-1$

The equation of the line passing through the point $(3,2)$ and having slope $-1$ is

$ y -2 = -1(x-3)$

$y-2=-x+3$

$ \Rightarrow x+y=5$

Hence B is the correct option.

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