Question

Draw the graph for the linear equation: $x=-2y$.
A.The line passes through $\left( 0,0 \right)$ and $m=\dfrac{1}{2}$.
B. the line passes through $\left( 0,-2 \right)$ and $m=-\dfrac{1}{2}$.
C. The line passes through $\left( 0,0 \right)$ and $m=-\dfrac{1}{2}$.
D. the line passes through $\left( -2,0 \right)$ and $m=-\dfrac{1}{2}$.

Answer 1

Hint : Change of form of the given equation will give the x-intercept and y-intercept of the line $x=-2y$. We change it to the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$ to find the x intercept, and y intercept of the line as $p$ and $q$ respectively. Then we place the points on the axes and from there we draw the line on the graph.

Complete step-by-step answer :
We are taking the general equation of line to understand the slope and the intercept form of the line $x=-2y$. The given equation is in the form of $y=mx+k$. m is the slope of the line. The slope of the line is $5$.
$\begin{aligned} & x=-2y \\\ & \Rightarrow y=-\dfrac{1}{2}x \\\ \end{aligned}$
The value of m is $m=-\dfrac{1}{2}$.
We have to find the x-intercept, and y-intercept of the line $x=-2y$.
We find the points which go through the line and satisfy the equation $x=-2y$.
We can see that $\left( 0,0 \right)$, $\left( 2,-1 \right)$, $\left( -4,2 \right)$ satisfies the equation $x=-2y$.
We now draw the line on the graph.

So, the correct answer is “Option C”.

Note : A line parallel to the X-axis does not intersect the X-axis at any finite distance. Hence, we cannot get any finite x-intercept of such a line. Same goes for lines parallel to the Y-axis. In case of slope of a line the range of the slope is 0 to $\infty$.