SAT Question e9908930: Linear Functions answer and explanation with Desmos solution

Choice B is correct. An equation that defines a linear function $f$ can be written in the form $f\left(x\right)=mx+b$, where $m$ and $b$ are constants. It's given in the table that when $x=-4$, $f\left(x\right)=0$. Substituting $-4$ for $x$ and $0$ for $f\left(x\right)$ in the equation $f\left(x\right)=mx+b$ yields $0=m\left(-4\right)+b$, or $0=-4m+b$. Adding $4m$ to both sides of this equation yields $4m=b$. Substituting $4m$ for $b$ in the equation $f\left(x\right)=mx+b$ yields $f\left(x\right)=mx+4m$. It's also given in the table that when $x=-\frac{19}{5}$, $f\left(x\right)=1$. Substituting $-\frac{19}{5}$ for $x$ and $1$ for $f\left(x\right)$ in the equation $f\left(x\right)=mx+4m$ yields $1=m\left(-\frac{19}{5}\right)+4m$, or $1=\frac{1}{5}m$. Multiplying both sides of this equation by $5$ yields $m=5$. Substituting $5$ for $m$ in the equation $f\left(x\right)=mx+4m$ yields $f\left(x\right)=5x+4\left(5\right)$, or $f\left(x\right)=5x+20$. If $h\left(x\right)=f\left(x\right)-13$, substituting $5x+20$ for $f\left(x\right)$ in this equation yields $h\left(x\right)=\left(5x+20\right)-13$, or $h\left(x\right)=5x+7$.