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Q.
The equation of straight line passing through $(2,1)$ and perpendicular to the line $x+y+7=0$ is
Straight Lines
Solution:
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
$y-1=(1)(x-2) \text { or } y-1=x-2 \Rightarrow x-y-1=0$