To determine which ordered pairs represent points on the graph of the equation $y = 3x + 2$, let's substitute each $x$-value into the equation and check if the resulting $y$-value matches the given point.

Step-by-step Check:

1. For (-5, -3): $y = 3(-5) + 2 = -15 + 2 = -13 \quad (\text{not } -3)$ Not on the graph.

2. For (3, 2): $y = 3(3) + 2 = 9 + 2 = 11 \quad (\text{not } 2)$ Not on the graph.

3. For (-6, 1): $y = 3(-6) + 2 = -18 + 2 = -16 \quad (\text{not } 1)$ Not on the graph.

4. For (1, 5): $y = 3(1) + 2 = 3 + 2 = 5 \quad (\text{matches } 5)$ This point is on the graph.

5. For (-1, -1): $y = 3(-1) + 2 = -3 + 2 = -1 \quad (\text{matches } -1)$ This point is on the graph.

6. For (-2, -4): $y = 3(-2) + 2 = -6 + 2 = -4 \quad (\text{matches } -4)$ This point is on the graph.

Correct Points:

The points that are on the graph of $y = 3x + 2$ are:

• $(1, 5)$
• $(-1, -1)$
• $(-2, -4)$

Conclusion:

You should select:

• $(1, 5)$
• $(-1, -1)$
• $(-2, -4)$

Let me know if you'd like further explanation or help with similar problems!

Related Questions:

1. How do you graph a linear equation like $y = 3x + 2$?
2. What does the slope $3$ represent in $y = 3x + 2$?
3. How do you find the y-intercept of a linear equation?
4. How can you determine if a point lies on a line algebraically?
5. What is the difference between a linear and a quadratic equation?

Tip:

When checking if a point lies on a graph, always substitute the $x$-value into the equation and verify the corresponding $y$-value.