sat-dog

Choice D is correct. It’s given that the graph shows the linear relationship between $x$ and $y$. The given graph passes through the points $\left(0,-5\right)$, $\left(1,-3\right)$, and $\left(2,-1\right)$. It follows that when $x=0$, the corresponding value of $y$ is $-5$, when $x=1$, the corresponding value of $y$ is $-3$, and when $x=2$, the corresponding value of $y$ is $-1$. Of the given choices, only the table in choice D gives these three values of $x$ and their corresponding values of $y$ for the relationship shown in the graph.

Choice A is incorrect. This table represents a relationship between $x$ and $y$ such that the graph passes through the points $\left(0,0\right)$, $\left(1,-7\right)$, and $\left(2,-9\right)$.

Choice B is incorrect. This table represents a relationship between $x$ and $y$ such that the graph passes through the points $\left(0,0\right)$, $\left(1,-3\right)$, and $\left(2,-1\right)$.

Choice C is incorrect. This table represents a linear relationship between $x$ and $y$ such that the graph passes through the points $\left(0,-5\right)$, $\left(1,-7\right)$, and $\left(2,-9\right)$.