Find equation of the line perpendicular to the line x – 7y + 5 = 0 and having x intercept 3.
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

$y=m(x-d)$

$\Rightarrow y=-7(x-3)$

$\Rightarrow y=-7 x+21$

$\Rightarrow 7 x+y=21$

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