Linear equations in two variables SAT question

Choice D is correct. The x-coordinate $a$ of the x-intercept $(a,0)$ can be found by substituting $0$ for $y$ in the given equation, which gives $7x+2(0)=-31$, or $7x=-31$. Dividing both sides of this equation by $7$ yields $x=-\frac{31}{7}$. Therefore, the value of $a$ is $-\frac{31}{7}$. The y-coordinate $b$ of the y-intercept $(0,b)$ can be found by substituting $0$ for $x$ in the given equation, which gives $7(0)+2y=-31$, or $2y=-31$. Dividing both sides of this equation by $2$ yields $y=-\frac{31}{2}$. Therefore, the value of $b$ is $-\frac{31}{2}$. It follows that the value of $\frac{b}{a}$ is $\frac{-\frac{31}{2}}{-\frac{31}{7}}$, which is equivalent to $(\frac{31}{2})(\frac{7}{31})$, or $\frac{7}{2}$.

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.