SAT Question 58c7daed: Linear Functions answer and explanation with Desmos solution

Choice A is correct. Since $h$ is a linear function, it can be defined by an equation of the form $h\left(x\right)=mx+b$, where $m$ and $b$ are constants. It's given that $h\left(0\right)=0$. Substituting $0$ for $x$ and $0$ for $h\left(x\right)$ in the equation $h\left(x\right)=mx+b$ yields $0=0m+b$, or $0=b$. Substituting $0$ for $b$ in the equation $h\left(x\right)=mx+b$ yields $h\left(x\right)=mx$. It's also given that $h\left(11\right)=10$. Substituting $11$ for $x$ and $10$ for $h\left(x\right)$ in the equation $h\left(x\right)=mx$ yields $10=11m$. Dividing both sides of this equation by $11$ yields $m=\frac{10}{11}$. Substituting $\frac{10}{11}$ for $m$ in the equation $h\left(x\right)=mx$ yields $h\left(x\right)=\frac{10}{11}x$. Therefore, an equation that defines $h$ is $h\left(x\right)=\frac{10}{11}x$.