SAT Question 6cb9bf45: Linear Inequalities answer and explanation with Desmos solution

Choice D is correct. A solution $(x,y)$ to the given inequality is a value of $x$ and the corresponding value of $y$ such that the value of $y$ is greater than the value of $7x-4$. All the tables in the choices have the same three values of $x$, so each of the three values of $x$ can be substituted in the given inequality to compare the corresponding values of $y$ in each of the tables. Substituting $3$ for $x$ in the given inequality yields $y>7(3)-4$, or $y>17$. Substituting $5$ for $x$ in the given inequality yields $y>7(5)-4$, or $y>31$. Substituting $8$ for $x$ in the given inequality yields $y>7(8)-4$, or $y>52$. Therefore, when $x=3$, $x=5$, and $x=8$, the corresponding values of $y$ must be greater than $17$, greater than $31$, and greater than $52$, respectively. In the table in choice D, when $x=3$, the corresponding value of $y$ is $21$, which is greater than $17$; when $x=5$, the corresponding value of $y$ is $35$, which is greater than $31$; when $x=8$, the corresponding value of $y$ is $56$, which is greater than $52$. Of the given choices, only choice D gives values of $x$ and their corresponding values of $y$ that are all solutions to the given inequality.