Question

What is the equation of the straight line which passes through the point of intersection of the straight lines $x+2y=5$ and $3x+7y=17$ and is perpendicular to the straight line $3x+4y=10$?

• A. $4x+3y+2=0$
• B. $4x-y+2=0$
• C. $4x-3y-2=0$
• D. $4x-3y+2=0$

Answer 1

Answer: (D)

$4x-3y+2=0$

The line $x+2y=5$ and $3x+7y=17$ intersect at the point $(1,2)$

Slope of line $3x+4y=10$ is $m=-\frac{3}{4}$

The slope of line perpendicular to $3x+4y=10$ is $m^{{}^{\prime }}=\frac{-1}{m}=\left(\frac{-1}{-\frac{3}{4}}\right)=\frac{4}{3}$

So, the equation of line through $(1,2)$ and having slope $\frac{4}{3}$ is

$(y-2)=\frac{4}{3}(x-1)$

$⟹3(y-2)=4(x-1)$

$⟹4x-3y+2=0$

The answer is option (D)