SAT Question b2fe7ab6: Linear Functions answer and explanation with Desmos solution

Choice D is correct. It's given that for the linear function $g$, the table shows four values of $x$ and their corresponding values of $g(x)$. It's also given that the function can be written as $g(x)=mx+b$, where $m$ and $b$ are constants. The table shows that when the value of $x$ is $1$, the corresponding value of $g(x)$ is $54$. Substituting $1$ for $x$ and $54$ for $g(x)$ in $g(x)=mx+b$ yields $54=m(1)+b$ or, $54=m+b$. Subtracting $b$ from both sides of this equation yields $54-b=m$. The table also shows that when the value of $x$ is $2$, the corresponding value of $g(x)$ is $51$. Substituting $2$ for $x$ and $51$ for $g(x)$ in $g(x)=mx+b$ yields $51=m(2)+b$, or $51=2m+b$. Substituting $54-b$ for $m$ in this equation yields $51=2(54-b)+b$. Applying the distributive property to the right-hand side of this equation yields $51=108-2b+b$, or $51=108-b$. Subtracting $108$ from both sides of this equation yields $-57=-b$. Dividing both sides of this equation by $-1$ yields $57=b$.