Question

The equation of the straight line which is perpendicular to $7x-8y=6$ and passing through $(-4,5)$ is

• A. $8x+7y=3$
• B. $7x+8y=3$
• C. $8x-7y=3$
• D. $7x-8y=3$

Answer 1

The correct option is A $8x+7y=3$

Given the equation of straight line is 7x-8y=6

Then $7x-8y=6$

$\Rightarrow -8y=-7x+6$

$\Rightarrow 8y=7x-6$

$\Rightarrow y=\frac{7}{8}x+\frac{6}{8}$

So the slope of the straight line is $\frac{7}{8}$

Then slope of line perpendicular this line is $-\frac{8}{7}$

Then equation of perpendicular line to this line passing through (-4,5) and slop is $-\frac{8}{7}$

$(y-5)=-\frac{8}{7}(x+4)$

$\Rightarrow 7(y-5)=-8(x+4)=7y-35=-8x-32$

$\Rightarrow 7y-35=-8x-32$

$\Rightarrow 7y+8x=-32+35$

$\Rightarrow 8x+7y=3$