Question

What is the slope of the tangent line of `x/(x-3y) = C`, where C is an arbitrary constant, at `(-2,1)`?

Answer 1

The given equation represents the straight line

`y = (1-1/C)/3x`. As C is fixed as 2/5, by setting (-2, 1) on the line,

the equation is `y = -x/2`. Its slope is `-1/2`.

Talking about tangent to a straight line.is tautology.