To determine which ordered pairs are solutions to the equation $y = -\frac{4}{3}x + \frac{2}{3}$, we need to plug each pair into the equation and check if they satisfy it.

Given pairs:

1. $(6, -1)$
2. $(2, -2)$
3. $(4, 5)$
4. $(-1, 2)$
5. $(-4, 6)$
6. $(5, -6)$

Let's evaluate each pair:

1. For $(6, -1)$: $y = -\frac{4}{3}(6) + \frac{2}{3} = -8 + \frac{2}{3} = -1$ The pair $(6, -1)$ satisfies the equation.

2. For $(2, -2)$: $y = -\frac{4}{3}(2) + \frac{2}{3} = -\frac{8}{3} + \frac{2}{3} = -2$ The pair $(2, -2)$ satisfies the equation.

3. For $(4, 5)$: $y = -\frac{4}{3}(4) + \frac{2}{3} = -\frac{16}{3} + \frac{2}{3} = -\frac{14}{3} \neq 5$ The pair $(4, 5)$ does not satisfy the equation.

4. For $(-1, 2)$: $y = -\frac{4}{3}(-1) + \frac{2}{3} = \frac{4}{3} + \frac{2}{3} = 2$ The pair $(-1, 2)$ satisfies the equation.

5. For $(-4, 6)$: $y = -\frac{4}{3}(-4) + \frac{2}{3} = \frac{16}{3} + \frac{2}{3} = \frac{18}{3} = 6$ The pair $(-4, 6)$ satisfies the equation.

6. For $(5, -6)$: $y = -\frac{4}{3}(5) + \frac{2}{3} = -\frac{20}{3} + \frac{2}{3} = -\frac{18}{3} = -6$ The pair $(5, -6)$ satisfies the equation.

Conclusion: The pairs that satisfy the equation are:

• $(6, -1)$
• $(2, -2)$
• $(-1, 2)$
• $(-4, 6)$
• $(5, -6)$

Would you like further clarification on any steps?

Here are five related questions you might find useful:

1. How can we determine if a point lies on the line of any given linear equation?
2. What does the slope $-\frac{4}{3}$ signify in this equation?
3. How do you find the y-intercept from an equation in slope-intercept form?
4. Can you explain the process of converting a linear equation to standard form?
5. How would you determine the x-intercept of this equation?

Tip: In a linear equation $y = mx + b$, the slope $m$ indicates the steepness and direction of the line, while $b$ is the y-intercept, where the line crosses the y-axis.