Question

Write the equation representing y-axis?

Answer 1

Hint: We need to write an equation representing the y-axis. We start to solve the given question by writing an equation of line parallel to the y-axis. Then, we substitute the value of $\left( x,y \right)$ as $\left( 0,0 \right)$ in the above equation to get the required result.

Complete step by step solution:
We need to find the equation representing the y-axis. We will be solving the given question by writing an equation of line parallel to the y-axis and substituting the value of $\left( x,y \right)$ as $\left( 0,0 \right)$ to get the equation representing y-axis.
In the cartesian coordinate system, the x-axis is the horizontal plane. It starts from negative infinity and continues till positive infinity.
In the cartesian coordinate system, the y-axis is the vertical plane. It starts from negative infinity and ends at positive infinity.
The x-axis and y-axis in the cartesian coordinate plane system are also called abscissa and ordinate respectively.
According to the question,
We need to find the equation representing the y-axis.
We know that the line equation of line to the y-axis is given by represented as follows,
$\Rightarrow x=k$
Here,
k is any constant term.
We know that y-axis passing through the point $\left( 0,0 \right)$
Now,
We need to substitute the value of $x$ in the above equation as $0$ .
Substituting the value of $x$ in the above line equation, we get,
$\Rightarrow 0=k$
From the above, we know that,
$\therefore k=0$
Substituting the value of $k$ in the line equation, we get,
$\Rightarrow x=k$
$\therefore x=0$
Thus, the equation representing the y-axis is $x=0$
The graph of the equation $x=0$ is represented diagrammatically as follows,

Note:The given question can be solved alternatively as follows,
For a line equation representing the y-axis, there is no deviation of the line from the vertical axis or y-axis. That means the value of $x$ would be zero throughout.
Hence, the equation representing the y-axis is given by $x=0$