SAT Question 0d5495a6: Linear Functions answer and explanation with Desmos solution

It's given that $h\left(0\right)=45$. Therefore, for the given function $h$, when $x=0$, $h\left(x\right)=45$. Substituting $0$ for $x$ and $45$ for $h\left(x\right)$ in the given function, $h\left(x\right)=x+b$, yields $45=0+b$, or $45=b$. Therefore, the value of $b$ is $45$.