I have a linear equation **10x - 15y - 6z = -30**. How many slopes are there for this given 3D plane equation? We know there are 3 intercepts in each dimensional axis. So, how do we find the slope of the plane? Please I need guidance about this. Thank you.

We generally define slopes only for lines (in 2D). I don’t think slopes are defined for planes in 3D, since we have better and simpler ways to do the same using the normal vector to the plane.

Even if say you need the slope of a line in a plane, one can ask with respect to what axis you want the slope?

(In 2D, it is a general standard to define the slope as the rate of change of y w.r.t. x. For example, if y increases at a faster rate compared to x, we say that the slope is greater than 1)

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Thank you for your reply.