to inverse-variance weighting, but additional weight is given for each spatial pixel based on the expected spatial profile for each source (which is a Gaussian for our unresolved sources), reducing statistical noise in the extracted spectra compared to a simple boxcar extraction scheme.

[ll]{}

$F_{\rm Ly\alpha}$ (10$^{-18}$ erg s$^{-1}$ cm$^{-2}$) & $5.5 \pm 0.9$ ($\pm 1.7$)\
Signal-to-noise Ratio & 6.5\
EW$_{\rm Ly\alpha}$ (Å) & 15.6$^{+5.9}_{-3.6}$ ($\pm 4.7$)\
$z_{\rm Ly\alpha}$ & $7.6637 \pm 0.0011$\
$\sigma_{\rm blue}$ (Å) & $0.33^{+5.51}_{-0.32}$\
$\sigma_{\rm red}$ (Å) & $6.49^{+0.32}_{-4.76}$\
FWHM$_{\rm red}$ (Å) & $15.0 \pm 2.7$\
$\sigma_{\rm red}$ (km s$^{-1}$) & $180 \pm 30$\
\
log $M_*$ ([$M_{\odot}$]{}) & $9.3^{+0.5}_{-0.4}$\
UV slope $\beta$ & $-2.2^{+0.3}_{-0.2}$\
$M_{\rm UV}$ & $-21.22^{+0.06}_{-0.10}$\
$E(B-V)$ & $0.06^{+0.10}_{-0.04}$\
SFR$_{\rm UV,obs}$ ([$M_{\odot}$]{}yr$^{-1}$) & $19^{+2}_{-1}$\
SFR$_{\rm UV,corr}$ ([$M_{\odot}$]{}yr$^{-1}$) & $33^{+56}_{-9}$

Correcting for telluric absorption was done using the @kurucz93 model spectrum of the spectral type of the slit star (G5I). Absolute flux calibration was performed by comparing and scaling the spectrum to the WFC3 $Y_{105}$-band magnitude of the slit star. This procedures accounts for the slit loss, assuming our targets are point sources unresolved under the seeing FWHM of our observations, which is a good approximation given the small size of high-redshift galaxies.

To 