Find real constants $c$ and $k$ such that $y=cx^k$ passes through point $(a, b)$ with slope $m$ In the Cartesian plane, can a power function of the form $y=cx^k$ (where $c&gt;0$ and $k&gt;1$, not necessarily an integer) be found such that its graph passes through any arbitrary point $(a, b)$ with arbitrary slope $m$? [Assume that $a&gt;0$, $b&gt;0$, and $m&gt;(b/a)$.] If so, how can $c$ and $k$ be calculated in terms of $a$, $b$, and $m$?

Note that this technique could be used to generate a type of spline curve that is tangent to each side of an obtuse angle, such as the one formed by the intersection of the lines $y=y_0$ and $y=mx$ (where $y_0&gt;0$ and $m&gt;0$).
The equations you get are

$$b=ca^k$$
$$m=cka^{k^-1}$$
dividing the first equation by the second yields
$$\frac{b}{m}=\frac{a}{k}$$
which can be solved for $k$, and you can then solve for c.
Let $f(x)=cx^k$. Then 1) $f(a)=b$ and 2) $f'(a)=m$