What is the equation of a line perpendicular to the line x – 7y + 5 = 0 and having x-intercept 3?

Let the slope of line be m

Here,

$m_{1}=\frac{-1}{-7}=\frac{1}{7}$

As lines are perpendicular,

$\therefore m_{1} \times m_{2}=-1$

$m \times \frac{1}{7}=-1$

$m=-7$

$\therefore$ Equation of line is

$\left(y-y_{1}\right)=m\left(x-x_{1}\right)$

$(y-0)=-7(x-3)$

$y=-7 x+21$

$\Rightarrow 7 x+y=21$