The problem asks us to identify which ordered pairs satisfy the equation $y = \frac{6}{7}x + 1$.

1. Problem Description

The problem asks us to identify which ordered pairs satisfy the equation $y = \frac{6}{7}x + 1$.

2. Solution Steps

To determine if an ordered pair $(x, y)$ satisfies the equation $y = \frac{6}{7}x + 1$, we substitute the $x$ and $y$ values into the equation and check if the equation holds true.

* (0, 1): $1 = \frac{6}{7}(0) + 1 \Rightarrow 1 = 0 + 1 \Rightarrow 1 = 1$. This is true.

* (4, -2): $-2 = \frac{6}{7}(4) + 1 \Rightarrow -2 = \frac{24}{7} + 1 \Rightarrow -2 = \frac{24}{7} + \frac{7}{7} \Rightarrow -2 = \frac{31}{7}$. Since $-2 = -\frac{14}{7}$, this is false.

* (-7, -5): $-5 = \frac{6}{7}(-7) + 1 \Rightarrow -5 = -6 + 1 \Rightarrow -5 = -5$. This is true.

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

* (0, 7): $7 = \frac{6}{7}(0) + 1 \Rightarrow 7 = 0 + 1 \Rightarrow 7 = 1$. This is false.

* (5, 4): $4 = \frac{6}{7}(5) + 1 \Rightarrow 4 = \frac{30}{7} + 1 \Rightarrow 4 = \frac{30}{7} + \frac{7}{7} \Rightarrow 4 = \frac{37}{7}$. Since $4 = \frac{28}{7}$, this is false.

Therefore, the ordered pairs that represent points on the graph of the equation are (0, 1) and (-7, -5).

3. Final Answer

(0, 1), (-7, -5)