Question

The equation of straight line passing through $(2,1)$ and perpendicular to the line $x+y+7=0$ is

• A. $x-y-1=0$
• B. $x+y+3=0$
• C. $x+y-3=0$
• D. $x-y+1=0$

Answer 1

Answer: (A)

Let $m$ be the slope of the line whose equation is to be found out which is perpendicular to the line $x+y+7=0$. The slope of the given line $y=(-1)x-7$ is $-1$. Therefore, using the condition of perpendicularity of lines, we have $m\times (-1)=-1$ or $m=1$.
Hence, the required equation of the line is
$y-1=(1)(x-2)\text{ or }y-1=x-2\Rightarrow x-y-1=0$