For an electron in different orbits of a hydrogen-like ion, which...

The kinetic energy $K$ of an electron in a hydrogen-like ion is given by:
$K = \dfrac{1}{4\pi\varepsilon_0} \dfrac{Ze^2}{2r}$

This shows that $K$ is inversely proportional to $r$, which can be written as $K = \dfrac{C}{r}$, where $C$ is a positive constant.

Taking the logarithm to the base 10 on both sides gives:
$\log_{10}(K) = \log_{10}(C) - \log_{10}(r)$

Comparing this with the equation of a straight line, $y = mx + c$, where $y = \log_{10}(K)$ and $x = \log_{10}(r)$, we get the slope $m = -1$.

Thus, the graph is a straight line with a slope of $-1$.

Answer: A straight line with a slope of $-1$