Question

the graph of $y = -\frac{1}{6}x - 4$ is shown on the grid. which ordered pair is in the solution set of $y leq -\frac{1}{6}x - 4$? options: $(-6, 0)$, $(6, -5)$, $(4, -6)$, $(2, -7)$

Explanation:

Step1: Substitute (-8,8) into inequality

Substitute $x=-8, y=8$ into $y > -\frac{1}{6}x - 4$:
$8 > -\frac{1}{6}(-8) - 4$
$8 > \frac{8}{6} - 4$
$8 > \frac{4}{3} - 4$
$8 > -\frac{8}{3}$
This is true.

Step2: Verify other options (check validity)

For (6,-5):
$-5 > -\frac{1}{6}(6) - 4$
$-5 > -1 - 4$
$-5 > -5$
This is false (not greater than).

For (4,-6):
$-6 > -\frac{1}{6}(4) - 4$
$-6 > -\frac{2}{3} - 4$
$-6 > -\frac{14}{3} \approx -4.67$
This is false.

For (-2,-7):
$-7 > -\frac{1}{6}(-2) - 4$
$-7 > \frac{1}{3} - 4$
$-7 > -\frac{11}{3} \approx -3.67$
This is false.

Answer:

A. $(-8,8)$