Question

How do you graph the function $y = 5$?

Answer 1

A graph is a visual diagram used to represent equations or functions or any statistical information through lines or curves. To plot a graph for an equation, we must know the coordinates of the graph. Coordinates of the graph can be found by assuming certain values for either $x$ or $y$ in the given equation and then finding out the value of another variable with the help of the first.
We must know that the function given in the question is a constant function. A constant function is a type of function whose output value is the same for every input value. It has the form of $y = c$ where $c$ is a constant. Here for $y = 5$, since whatever be the value of $x$, the value of $y$ will be $5$ only.

Complete Step by Step Solution:
The given equation for which the graph shall be plotted is $y = 5$. Since whatever be the value of $x$, the value of $y$ will only be $5$. Therefore the coordinates of the graph for $y = 5$ will be in the form of $(x,5)$ where $x$ can assume any value.
Hence, the graph will be a horizontal line passing through the $y$-axis which will be at a distance of $5$ units from the origin $(0,0)$. The coordinates of the point at which the graph will intersect the $y$-axis are $(0,4)$as the value of $x$ coordinates on the $y$-axis are $0$.
With the help of all the information, we can plot the required graph as given below:

Note:
It is fascinating to know that the graph of both the $x$-axis and $y$-axis can also be defined. The graph of $y$-axis is expressed as $x = 0$ whereas the graph of $x$-axis is expressed as $y = 0$.