Question

Which of the following options is true for the equation $x+2y=0$?

• A. The line passes through $(0,\frac{-1}{2})$ and $m=\frac{-1}{2}$
• B. The line passes through $(2,-1)$ and $m=\frac{-1}{2}$
• C. The line passes through $(0,0$) and $m=\frac{1}{2}$
• D. The line passes through $(0,0)$ and $m=\frac{-1}{2}$

Answer 1

The correct option is B The line passes through $(2,-1)$ and $m=\frac{-1}{2}$

Given linear equation is $x+2y=0$ i.e. $y=\frac{-1}{2}x$

$x$ is independent and $y$ is dependent variable.

Let's assign some values to $x$ and find the corresponding values of $y$

$x$ $2$ $4$ $-2$ $-4$

$y$ $-1$ $-2$ $1$ $2$

So, the ordered pair of values of $(x,y)$ are $(2,-1),(4,-2),(-2,1),(-4,2)$

Let's plot these points on a graph and then we get the above graph image

We get the slope as $\frac{-1}{2}$ and it passes through $(2,-1)$ and $(0,0)$.

Hence, options B and D are correct.