Question

The intercept cut off from $y-$axis is twice that from $x-$axis by the line and the line is passing through $\left(1,2\right)$ then its equation is

• 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

$2x+y=4$

Explanation for the correct answer:

Step 1:Assume intercepts and form equation using double intercept form

Let us assume that, the $x-$intercept of the given straight line is $a$.

As the $y-$intercept of the given straight line is twice the $x-$intercept.

Thus, $y-$intercept, $b=2a$.

The intercept form of a straight line can be given by $\frac{x}{a}+\frac{y}{b}=1$.

Thus, $\frac{x}{a}+\frac{y}{2a}=1$

$$\begin{gathered} \Rightarrow \frac{2x+y}{2a}=1 \\ \Rightarrow 2x+y=2a \end{gathered}$$

Step 2: Substitute the co-ordinates of the point to obtain the value of intercepts

It is given that, the line is passing through $\left(1,2\right)$.

So, the given equation satisfies the point $\left(1,2\right)$.

Thus, $2\left(1\right)+2=2a$

$$\begin{gathered} \Rightarrow 2a=4 \\ \Rightarrow a=\frac{4}{2} \\ \Rightarrow a=2 \end{gathered}$$

Step 3: Write the equation of the line

Thus, the equation of the straight line can be given by, $2x+y=2a$.

Substitute $a$ with $2$.

$$\begin{gathered} \Rightarrow 2x+y=2\left(2\right) \\ \Rightarrow 2x+y=4 \end{gathered}$$

Therefore, the equation of the straight line is $2x+y=4$.