Question

If a line passes through the intersection point of the graphs of the lines $x+2y=7$ and $x-y=4$ and the origin, then find the equation of the line.

• A. $y=0.5x$
• B. $y=5x$
• C. $y=0.2x$
• D. $y=-2x$

Answer 1

The correct option is C $y=0.2x$

Given lines are $x+2y=7$ ......... (1) and $x-y=4$ ........ (2)

To find the point of intersection, we need to solve the equations simultaneously.

from eq(2) we get x = y + 4

substitute the value of x in the eq(1) we get the value of y and then we can get the value of x from any equation, so

By solving the equations (1) and (2) we get

$x=5$ and $y=1$.

So, the point of intersection is $(5,1)$

Equation of line passing through $(5,1)$ and $(0,0)$ will be

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$

$⟹$ $\frac{y-1}{x-5}=\frac{-1}{-5}$

$⟹$ $5y-5=x-5$

$\therefore y=0.2x$ is the required equation of the line.