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

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.