Question

The equation of the straight line joining the origin to the point of intersection of $y-x+7=0$ and $y+2x-2=0$ is

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

Answer 1

The correct option is D

$4x+3y=0$

Find the equation of the straight line based on given information

Given intersecting lines,

$y-x=-7...\left(i\right)$

$y+2x=2...\left(ii\right)$

Subtracting $\left(i\right)$ from $\left(ii\right)$ we get

$3x=9$

$\therefore x=3$

Re-substituting this value of $x$ in $\left(i\right)$

$y=-4$

$\therefore (3,-4)$ is the point of intersection of the given lines

Equation of line between $(0,0)$ and $(3,-4)$ is given by two point form of a line as

$\frac{y-0}{-4-0}=\frac{x-0}{3-0}$

$\Rightarrow$ $4x+3y=0$

Hence option $\left(D\right)$ is the correct answer.