Question:
Find equation of the line perpendicular to the line $x-7 y+5=0$ and having $x$ intercept 3 .
Solution:
The given equation of line is $x-7 y+5=0$.
Or, $y=\frac{1}{7} x+\frac{5}{7}$, which is of the form $y=m x+c$
$\therefore$ Slope of the given line $=\frac{1}{7}$
The slope of the line perpendicular to the line having a slope of $\frac{1}{7}$ is $m=-\frac{1}{\left(\frac{1}{7}\right)}=-7$
The equation of the line with slope $-7$ and $x$-intercept 3 is given by
$y=m(x-d)$
$\Rightarrow y=-7(x-3)$
$\Rightarrow y=-7 x+21$
$\Rightarrow 7 x+y=21$