Question

The intercept made by a line on y-axis is double to the intercept made by it on x-axis. If it passes through $(1,2)$ then its equation.

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

Answer 1

The correct option is A $2x+y=4$

Let the intercept made on $x-axis=K,$

The intercept made on $y-axis=2K$

We know that if a line has $x$ and $y$ intercepts as $a$ & $b$ then the equation of the line is, $\frac{x}{a}+\frac{y}{b}=1.$ Here, $a=K,b=2K.$

$\frac{x}{K}+\frac{y}{2K}=1⟶\left(1\right)$

Given that the line passes through the point $(1,2)$ Then its' equation is,

Substituting $(1,2)$ in equation $\left(1\right),$

We get $2\times 1+2=2K4=2KK=2$

Substituting $K=2$ in equation $\left(1\right),$

We get $2x+y=2\times 2$

$\therefore$ Equation of line is $2x+y=4.$