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A homology class $d\in {\mathrm{\text{H}}}_2(X,\mathbb{Z})$ of a complex flag variety $X=G∕P$ is called a line degree if the moduli space ${\overline{\mathcal{ℳ}}}_{0,0}(X,d)$ of 0-pointed stable maps to X of degree d is also a flag variety $G∕P^{\prime }$. We prove a quantum equals classical formula stating that any n-pointed (equivariant, $\mathrm{\text{K}}$-theoretic, genus zero) Gromov–Witten invariant of line degree on X is equal to a classical intersection number computed on the flag variety $G∕P^{\prime }$. We also prove an n-pointed analogue of the Peterson comparison formula stating that these invariants coincide with Gromov–Witten invariants of the variety of complete flags $G∕B$. Our formulas make it straightforward to compute the big quantum $\mathrm{\text{K}}$-theory ring ${\mathrm{\text{QK}}}^{\mathrm{\text{big}}}(X)$ modulo the ideal $〈Q^d〉$ generated by degrees d larger than line degrees.