Question

How do you find the slope of $y = 0$ ?

Answer 1

Compare the given equation i.e. $y = 0$ with the general form i.e. $y = mx + c$ , after that you will directly get the slope. Or you can also check whether the given equation is of horizontal or vertical line and after that write directly the slope.

Complete step by step solution:
The given equation is $y = 0$
We can rewrite the given equation as $y = 0.x + 0$
The general equation of a straight line is $y = mx + c$ , where m is the slope of line, also known as gradient and c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis
Now, by comparing given equation with general equation, we get
Slope (m) $= 0$ and y-intercept (c) $= 0$

Additional Information:
You can also write directly about the slope in questions in which we have equations like $x = 0$ and $y = 0$. As we know that $x = 0$ describes a vertical line, therefore its slope will be $\infty$ and $y = 0$ describes a horizontal line, therefore its slope will be 0.

Note:
There is an alternative method in which we apply formula of slope (m) i.e. slope (m) $= {\tan ^{ - 1}}\left( {\dfrac{y}{x}} \right)$.
As you can see $y = 0$ describes a horizontal line i.e. x-axis
Now, as we know that slope (m) $= {\tan ^{ - 1}}\left( {\dfrac{y}{x}} \right)$
Now, here $y = 0$ and x can be any value
Therefore, slope (m) $= {\tan ^{ - 1}}\left( {\dfrac{0}{x}} \right)$
$\Rightarrow slope\left( m \right) = {\tan ^{ - 1}}\left( 0 \right)$
$\Rightarrow slope\left( m \right) = 0$