SAT Question 48fb34c8: Linear Inequalities answer and explanation with Desmos solution

Choice D is correct. 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 $y>13\left(3\right)-18$, or $y>21$. Therefore, when $x=3$, the corresponding value of $y$ is greater than $21$. Substituting $5$ for $x$ in the given inequality yields $y>13\left(5\right)-18$, or $y>47$. Therefore, when $x=5$, the corresponding value of $y$ is greater than $47$. Substituting $8$ for $x$ in the given inequality yields $y>13\left(8\right)-18$, or $y>86$. Therefore, when $x=8$, the corresponding value of $y$ is greater than $86$. For the table in choice D, when $x=3$, the corresponding value of $y$ is $26$, which is greater than $21$; when $x=5$, the corresponding value of $y$ is $52$, which is greater than $47$; when $x=8$, the corresponding value of $y$ is $91$, which is greater than $86$. Therefore, the table in choice D gives values of $x$ and their corresponding values of $y$ that are all solutions to the given inequality.