Question

The equation of the line with slope $-\frac{3}{2}$ and which is concurrent with the lines $4x+3y-7=0$ and $8x+5y-1=0$ is

• A. $3x+2y-63=0$
• B. $3x+2y-2=0$
• C. $2y-3x-2=0$
• D. none of these

Answer 1

The correct option is B

$3x+2y-2=0$

Given :

$4x+3y-7=0...\left(1\right)$

$8x+5y=0...\left(2\right)$

The equation of the line with slope $-\frac{3}{2}$ is given below :

$y=-\frac{3}{2}x+c$

$\Rightarrow \frac{3}{2}x+y-c=0...\left(3\right)$

The lines (1), (2) and (3) are concurrent.

$\left|\begin{array}{ccc}4& 3& -7\\ 8& 5& -1\\ \frac{3}{2}& 1& -c\end{array}\right|=0$

$\Rightarrow 4(-5c+1)-3(-8c+\frac{3}{2})-7(8-\frac{15}{2})=0$

$\Rightarrow -20c+4+24c-\frac{9}{2}-56+\frac{105}{2}=0$

$\Rightarrow \frac{-40c+8+48c-9-112+105}{2}=0$

$\Rightarrow 8c=8$

$\Rightarrow c=1$

On substituting $c=1$ in $y=-\frac{3}{2}x+c,$ we get:

$y=-\frac{3}{2}x+1$

$\Rightarrow 3x+2y-2=0$