Question

How do you graph the line $y = 3$?

Answer 1

Hint: The given equation of the line is independent of $x$ variable. Hence, we can say that this line is parallel to the $X$ axis but passing through points with constant $y$ coordinates.

Formulas used: The standard given of a line passing through a point $\left( {x,y} \right)$, $y = mx + c$, where $m$ is the slope of the line and $c$ is the $y$-intercept.

Complete step-by-step answer:
We know that,
$y = mx + c$ ------(1)
is the standard equation of a line.
Here, we are given the equation
$y = 3$-----------(2)
Comparing equations (1) and (2), we can say that,
$m = 0$ and $c = 3$.
That is, the slope of the line is zero.
$ \Rightarrow $ The line is parallel to the $X$ axis.
Also, the line has $y$-intercept at $\left( {0,3} \right)$.
Thus, we can conclude that $y = 3$ is a line having slope zero and passing through $\left( {0,3} \right)$.
Now, let us plot the line in a graph as shown:

Additional information:
The standard equations of some special lines:
Parallel to $X$ axis: $y = a$, where $a$ is any constant.
Parallel to $Y$ axis: $x = b$, where $b$ is any constant.
Passing through the origin: $y = mx$, where $m$ is the slope of the line.

Note: The plotting of a line requires at least one of the following requirement as below:
There must be at least two distinct points.
There must be an equation of the line.