Question

1. the graph of ( y = -\frac{1}{6}x - 4 ) is shown on the grid. which ordered pair is in the solution set of ( y > -\frac{1}{6}x - 4 )? options: ( (-8, -8) ), ( (6, -5) ), ( (-2, -7) ), ( (4, -6) )

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 (optional check)

Substitute $(0,-5)$:
$-5 > -\frac{1}{6}(0) - 4$
$-5 > -4$
This is false.

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

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

Answer:

(-8,8)