Question

How do you graph $y - x = 0$?

Answer 1

Hint: The given equation is a linear equation. In order to draw a graph of a linear equation, firstly we assume some value of either of the variables, $x$ or $y$. Then we use these values by substituting them in the given linear equation. Next, we plot these points in the$x - y$plane. Then, we will have our required graph of the given linear equation.

Complete step by step answer:
The linear equation is $y - x = 0$.
We have to graph the given equation.
The given linear equation can be rewritten as: add variable $x$ on both sides of the equation, so that the variable $y$ gets isolated on the left-hand side of the equation and moreover, the equation is balanced at the same time.
$
   \Rightarrow y - x + x = 0 + x \\
   \Rightarrow y = x \\
 $
From the above obtained equation, we can say that both $x$ and $y$ coordinates are equal.
To draw a graph, we need some points. Let’s find out some points by choosing different values of $x$.
If$x = 0$, then$y = 0$ (as $y = x$)
If$x = 2$, then$y = 2$ (as $y = x$)
If$x = - 2$, then$y = - 2$ (as $y = x$)

$x$	$0$	$2$	$ - 2$
$y$	$0$	$2$	$ - 2$
Point	$\left( {0,0} \right)$	$\left( {2,2} \right)$	$\left( { - 2, - 2} \right)$

Now, we plot these three coordinates in the graph. Draw a straight line through these points.

Thus, this is our required graph.

Note: The graph of a linear equation is always a straight line. Students can check that the points found by them are correct or not by seeing if all the points obtained after calculations lie on a straight line or not. If not, then the points calculated are wrong. So, it is advised to do calculations carefully while finding out the points and plotting in $x - y$ plane.