which table shows a negative correlation?\n|x|2|5|6|7|10|12|\n|y|-8|-5|-6|-3|-2|-1|\n|x|2|5|6|7|10|12|\n|y|-5…

Explanation:

Step1: Recall negative - correlation concept

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

Step2: Analyze the first table

As $x$ increases from 2 to 12 ($2,5,6,7,10,12$), $y$ values are $- 8,-5,-6,-3,-2,-1$. The $y$ - values do not show a consistent decrease.

Step3: Analyze the second table

All $y$ - values are $-5$ regardless of the $x$ - values. There is no correlation.

Step4: Analyze the third table

As $x$ increases from 2 to 12, $y$ values are $6,3,1,1,3,6$. The $y$ - values do not show a consistent decrease.

Step5: Analyze the fourth table

As $x$ increases from 2 to 12 ($2,5,6,7,10,12$), $y$ values are $4,2, - 4,-3,-11,-12$. The $y$ - values generally decrease as $x$ increases.

Answer:

The fourth table (with $x$ values 2, 5, 6, 7, 10, 12 and $y$ values 4, 2, - 4, - 3, - 11, - 12) shows a negative correlation.