Question

The equation of the straight line passing through the point $(3,2)$ and perpendicular to the line $y=x$ is

• A. $x+y=1$
• B. $x-y=5$
• C. $x+y=5$
• D. $x-y=1$

Answer 1

The correct option is C $x+y=5$

Given line : $y=x$

$\Rightarrow$ Slope is $1$,

If two lines are perpendicular, then product of their slopes $=-1$

So, slope of the line perpendicular to given line is $-1$.

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

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

$\Rightarrow y-2=-x+3$

$\therefore x+y=5$

Hence, option $\left(B\right)$ is correct.