  We motivate a minimal realization of slow-roll $k$-inflation by incorporating
the local conformal symmetry and the broken global $\mathrm{SO}(1,1)$ symmetry
in the metric-affine geometry. With use of the metric-affine geometry where
both the metric and the affine connection are treated as independent variables,
the local conformal symmetry can be preserved in each term of the Lagrangian
and thus higher derivatives of scalar fields can be easily added in a
conformally invariant way. Predictions of this minimal slow-roll $k$-inflation,
$n_\mathrm{s}\sim 0.96$, $r\sim 0.005$, and $c_\mathrm{s}\sim 0.03$, are not
only consistent with current observational data but also have a prospect to be
tested by forthcoming observations.
