The given equation is $y = \frac{1}{3}x$. To determine which ordered pairs satisfy this equation, we will substitute the $x$-value of each pair into the equation and see if the resulting $y$-value matches.

Verification:

1. For $(-6, -2)$: $y = \frac{1}{3}(-6) = -2$ This is correct.

2. For $(-6, 5)$: $y = \frac{1}{3}(-6) = -2 \neq 5$ This is incorrect.

3. For $(6, 2)$: $y = \frac{1}{3}(6) = 2$ This is correct.

4. For $(3, 1)$: $y = \frac{1}{3}(3) = 1$ This is correct.

5. For $(0, 0)$: $y = \frac{1}{3}(0) = 0$ This is correct.

6. For $(-3, -1)$: $y = \frac{1}{3}(-3) = -1$ This is correct.

Correct Answers:

• $(-6, -2)$
• $(6, 2)$
• $(3, 1)$
• $(0, 0)$
• $(-3, -1)$

Let me know if you'd like further clarification or additional help!

Related Questions:

1. How can you find the slope of a line from its equation?
2. What does the slope represent in this context?
3. How would this equation change if the slope were doubled?
4. How can you verify a point lies on a graph without substitution?
5. What are other forms of linear equations besides slope-intercept form?

Tip:

When testing points against an equation, substitution is a quick and accurate way to verify their validity!