Question

The equation of the line passing through the point $(2,3)$ and the point of intersection of lines $2x-3y-7=0$ and $7x+4y+2=0$ is

• A. $35x-9y-43=0$
• B. $21x-46y-96=0$
• C. $46+21y-155=0$
• D. $46x-21y-29=0$

Answer 1

The correct option is A $35x-9y-43=0$

Point of intersection of lines $2x-3y-7=0$ and $7x+4y+2=0$ is $(\frac{22}{29},\frac{-159}{87})$.

Thus slope of line passing through point $(\frac{22}{29},\frac{-159}{87})$ and $(2,3)$ is:

m = $\frac{3-\left(\frac{-159}{87}\right)}{2-\frac{22}{29}}=\frac{35}{9}$

So equation of line is $(y-3)=m(x-2)$

Or, $35x-9y-43=0$