The problem asks us to identify which of the given ordered pairs are solutions to the equation $-\frac{5}{6}x = y + \frac{1}{6}$. We can determine this by plugging the $x$ and $y$ values of each ordered pair into the equation and checking if the equation holds true.

1. Problem Description

The problem asks us to identify which of the given ordered pairs are solutions to the equation $-\frac{5}{6}x = y + \frac{1}{6}$. We can determine this by plugging the $x$ and $y$ values of each ordered pair into the equation and checking if the equation holds true.

2. Solution Steps

The given equation is:

$-\frac{5}{6}x = y + \frac{1}{6}$.

Let's test each ordered pair:

(0, 2): $-\frac{5}{6}(0) = 2 + \frac{1}{6} \implies 0 = \frac{13}{6}$. This is false.

(1, -1): $-\frac{5}{6}(1) = -1 + \frac{1}{6} \implies -\frac{5}{6} = -\frac{5}{6}$. This is true.

(6, 7): $-\frac{5}{6}(6) = 7 + \frac{1}{6} \implies -5 = \frac{43}{6}$. This is false.

(-5, -6): $-\frac{5}{6}(-5) = -6 + \frac{1}{6} \implies \frac{25}{6} = -\frac{35}{6}$. This is false.

(-7, 5): $-\frac{5}{6}(-7) = 5 + \frac{1}{6} \implies \frac{35}{6} = \frac{31}{6}$. This is false.

(-5, 4): $-\frac{5}{6}(-5) = 4 + \frac{1}{6} \implies \frac{25}{6} = \frac{25}{6}$. This is true.

3. Final Answer

The ordered pairs that are solutions to the equation are (1, -1) and (-5, 4).