Question

What is the slope of the line $y=\dfrac{4}{5}$?

Answer 1

Hint: In this problem we need to find the slope of the given line. Generally, the slope of the line is easily calculated from its slope intercept form which is given by $y=mx+c$ where $m$ is the slope of the line and $c$ is the $y$ intercept of the line. So, we will first compare the given equation of the line with the slope intercept form and write the values of slope $m$ and $y$ intercept.

Complete step-by-step answer:
Given line is $y=\dfrac{4}{5}$.
The graph of the given line will be

In the above equation we can observe that the equation of the line does not have any $x$ variable. So, we are going to add the term $0x$ which is equal to $0$, so that there will be no change in the value of the equation, then the given equation is modified as
$y=0x+\dfrac{4}{5}$
We have the equation of the line in slope intercept form as $y=mx+c$ where $m$ is the slope of the line and $c$ is the $y$ intercept of the line.
Comparing the equation $y=0x+\dfrac{4}{5}$ with the equation $y=mx+c$, then we will get
$m=0$, $c=\dfrac{4}{5}$.
Hence the slope of the given line $y=\dfrac{4}{5}$ is $0$.

Note: We can also simplify say that the lines which are parallel to $x$ axis which are given by $y=c$ have zero slope and the lines which are parallel to $y$ axis which are given by $x=c$ have an infinite slope where $c$ is the constant in the equations $y=c$, $x=c$.