Question

The equation of the straight line which passes through the point $(1,-2)$ and cuts off equal intercepts from axes, is

• A. $x+y=1$
• B. $x-y=1$
• C. $x+y+1=0$
• D. $x–y–2=0$

Answer 1

The correct option is C

$x+y+1=0$

Find the equation of the straight line based on given information

We know that, the equation of line in intercept form is

$\frac{x}{a}+\frac{y}{b}=1$

Given line cuts off equal intercepts. So $a=b$

$$\begin{gathered} \Rightarrow \frac{x}{a}+\frac{y}{a}=1 \\ \Rightarrow x+y=a...\left(\mathrm{i}\right) \end{gathered}$$

It is given that it passes through point $(x,y)=(1,-2)$.

$$\begin{gathered} \Rightarrow 1-2=a \\ \Rightarrow a=-1 \end{gathered}$$

By substituting the value of $a$ in eq. $\left(\mathrm{i}\right)$ we get,

$$\begin{gathered} x+y=-1 \\ \Rightarrow x+y+1=0 \end{gathered}$$

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