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Choose the correct answer from the given four options. The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is

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

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Toolbox:
• 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.
answered Jul 3, 2014

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