The slope of  x -axis is zero and the slope of  y -axis is not defined.  HOW AND WHY ??

The said line in our study material is: 

slope of x-axis is zero and the slope of y-axis is not defined.

Here, we are talking about the slope of both the axis with respect to horizontal.

In case of x-axis, θ = 0° and in case of y -axis, θ = 90°.

So, slope of x -axis = tan θ  = tan 0° = 0

Similarly, slope of y -axis = tan θ  = tan 90° and we know that value of tan 90° is undefined.

So, this is the only reason why slope of y-axis is undefined.

Hope you get it!!