If a graph is plotted between ${\mathrm{T}}^2 \mathrm{and} {{\mathrm{r}}^3}_{ }$for a planet, then its slope will be (where ${\mathrm{M}}_{\mathrm{S}}$ is the mass of the sun)

Time period of a revolution of a planet,

$\mathrm{T} = \frac{2\mathrm{\pi r}}{\mathrm{v}} = \frac{2\mathrm{\pi r}}{\sqrt{{\displaystyle \frac{{\mathrm{GM}}_{\mathrm{s}}}{\mathrm{r}}}} } = \frac{2{\mathrm{\pi r}}^{{\displaystyle \frac{3}{2}}}}{\sqrt{{\mathrm{GM}}_{\mathrm{S}}}}$

where ${\mathrm{M}}_{\mathrm{S}}$ is the mass of the sun.
Squaring both sides, we get

${\mathrm{T}}^2 = \frac{4{\mathrm{\pi }}^2{\mathrm{r}}^3}{{\mathrm{GM}}_{\mathrm{S}}}$

The graph between ${\mathrm{T}}^2 \mathrm{and} {\mathrm{r}}^3$ is a straight line whose slope is $\frac{4{\mathrm{\pi }}^2}{{\mathrm{GM}}_{\mathrm{S}}}$.