Question

What is the nature of graph for $x+y=0$?

• A. Curved line
• B. Parabola
• C. Circle
• D. Straight line

Answer 1

The correct option is D Straight line

The given equation is $x+y=0$.

Our intention is to find out the values of $y$ by substituting different values of $x$ as per the following table in $x+y=0$. And, after getting the ordered pairs $(x,y)$, we can plot in cartesian plane to get the nature of graph.

x	y
0	?
1	?
2	?
-1	?
-2	?

Substituting the values of $x$ in $x+y=0$ to find $y$:
$\bullet$ For $x=0,0+y=0\Rightarrow y=0$
$\bullet$ For $x=1,1+y=0\Rightarrow y=-1$
$\bullet$ For $x=2,2+y=0\Rightarrow y=-2$
$\bullet$ For $x=-1,-1+y=0\Rightarrow y=1$
$\bullet$ For $x=-2,-2+y=0\Rightarrow y=2$

It is very clear from the above calculation that the values of $y$ are just the opposite of the values of $x$ as $x+y=0\Rightarrow y=-x$. So, we get the whole bunch of ordered pairs as

Ordered Pair	x	y
$(0,0)$	0	0
$(1,-1)$	1	-1
$(2,-2)$	2	-2
$(-1,1)$	-1	1
$(-2,2)$	-2	2

After plotting the ordered pairs in cartesian plane and by joining the points, we get


All these ordered pairs seem to line up along a line. So, we can connect them through a straight line, and that diagonal straight line passes through the origin.

$\therefore$ We can conclude that the nature of the graph of $x+y=0$ is a $\underset{–}{\text{straight line}}$, which passess through the origin.