Final answer:
The ordered pair that satisfies the inequality y > -1/6x - 4 is A. (-8, 8), as it is the only pair that makes the inequality true when the values are substituted into the equation.
Step-by-step explanation:
To find out which ordered pair is a solution to the inequality y > -1/6x - 4, we need to substitute the x and y values from each ordered pair into the inequality and see if the inequality holds true.
For the ordered pair (-8, 8), we substitute x with -8 and y with 8:
8 > -(-1/6)(-8) - 4 -> 8 > 4/3 - 4 -> 8 > -8/3, which is true.
For the ordered pair (6, -5), we substitute x with 6 and y with -5:
-5 > -1/6(6) - 4 -> -5 > -1 - 4 -> -5 > -5, which is not true because the inequality is strict (not "greater than or equal to").
For the ordered pair (4, -6), we substitute x with 4 and y with -6:
-6 > -1/6(4) - 4 -> -6 > -2/3 - 4 -> -6 > -14/3, which is not true.
For the ordered pair (-2, -7), we substitute x with -2 and y with -7:
-7 > -1/6(-2) - 4 -> -7 > 1/3 - 4 -> -7 > -11/3, which is not true.
The only ordered pair that satisfies the inequality is A. (-8, 8).