Question

The line $ x + 2y = 0 $
A.The line passes through $ (0,0) $ and $ m = - 3 $
B.The line passes through $ (0,0) $ and $ m = - \dfrac{1}{2} $
C.The line passes through $ (0,0) $ and $ m = 3 $
D.None of these.

Answer 1

Hint: The given question asks us to evaluate the properties of the given line. We know it is an equation of line from the fact that the given equation is linear in both the variables $ x $ and $ y $ . Thus we know that the given equation is of a line. Now all the three options given in the question talk about its passing through a point all of them say $ (0,0) $ so we will put these values and see if the equation is correct if it is then we can write that it passes through that point. To find the value of $ m $ which is given by the slope in geometrical terms we know that the value of $ m $ of a line is calculated by finding $ \dfrac{y}{x} $ which will give us the value of $ m $ in the given question. Thus we will get the value of $ m $ as well and will thus be able to choose the correct option.

Complete step-by-step answer:
 First we will check whether the point $ (0,0) $ passes through the line .
We will put value of $ (0,0) $ into the line’s equation
 $ x + 2y = 0 $
We get,
 $ 0 + 2 \times 0 = 0 $
 $ 0 = 0 $
Hence the given line passes through $ (0,0) $
For the slope,
 $ x + 2y = 0 $
 $ \dfrac{x}{{2y}} = - 1 $
 $ \dfrac{x}{y} = - 2 $
 $ \dfrac{y}{x} = - \dfrac{1}{2} $
Hence slope is $ - \dfrac{1}{2} $
Hence the option B is correct for this questions which states that
The line passes through $ (0,0) $ and $ m = - \dfrac{1}{2} $
So, the correct answer is “Option B”.

Note: Remember whenever the equation of line of the form:
 $ y = mx + c $
This form is called the slope intercept form of line here $ m $ is the slope of line, and the value of $ c $ is the $ y - {\text{intercept}} $ of the line. The intercept is the point at which the line cuts the axes.