which table shows a negative correlation?

Explanation:

Step1: Recall negative - correlation concept

In a negative correlation, as the value of $x$ increases, the value of $y$ decreases.

Step2: Analyze the first table

As $x$ values ($2,5,6,7,10,12$) increase, $y$ values ($- 8,-5,-6,-3,-2,-1$) do not consistently decrease. For example, when $x$ goes from $5$ to $6$, $y$ goes from $-5$ to $-6$ and then when $x$ goes from $6$ to $7$, $y$ goes from $-6$ to $-3$.

Step3: Analyze the second table

As $x$ values ($2,5,6,7,10,12$) increase, $y$ values ($4,2, - 4,-3,-11,-12$) generally decrease.

Step4: Analyze the third table

As $x$ values ($2,5,6,7,10,12$) increase, $y$ values ($6,3,1,1,3,6$) do not decrease. They first decrease from $6$ to $1$ and then increase.

Step5: Analyze the fourth table

As $x$ values ($2,5,6,7,10,12$) increase, $y$ values ($-6,-5,-5,-6,-6,-6$) do not show a clear decreasing trend.

Answer:

The second table shows a negative correlation.