let $x=\mathrm{sl}_3(\mathbb{r})/\mathrm{sl}_3(\mathbb{z})$ and $a(t)=\mathrm{diag}(t^2,t^{-1},t^{-1})$. the expanding horospherical group $u^+$ is isomorphic to $\mathbb{r}^2$. a result of shah tells us that the $a(t)$-translates of a non-degenerate real-analytic curve in a $(u^+)$-orbit get equidistributed in $x$. it remains to study degenerate curves, i.e. planar lines $y=ax+b$. in this talk, we give a diophantine condition on the parameter $(a,b)$ which serves as a necessary and sufficient condition for equidistribution. \\ \\ joint work with kleinbock, saxcé and shah. if time permits, i will also talk about generalisations to $\mathrm{sl}_n(\mathbb{r})/\mathrm{sl}_n(\mathbb{z})$. joint work with shah.