Linear functions SAT question

Choice D is correct. Since $f$ is a linear function, it can be defined by an equation of the form $f(x)=ax+b$, where $a$ and $b$ are constants. It's given that $f(0)=8$. Substituting $0$ for $x$ and $8$ for $f(x)$ in the equation $f(x)=ax+b$ yields $8=a(0)+b$, or $8=b$. Substituting $8$ for $b$ in the equation $f(x)=ax+b$ yields $f(x)=ax+8$. It's given that $f(1)=12$. Substituting $1$ for $x$ and $12$ for $f(x)$ in the equation $f(x)=ax+8$ yields $12=a(1)+8$, or $12=a+8$. Subtracting $8$ from both sides of this equation yields $a=4$. Substituting $4$ for $a$ in the equation $f(x)=ax+8$ yields $f(x)=4x+8$. Therefore, an equation that defines $f$ is $f(x)=4x+8$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.