We are asked to check which of the given points is a solution to the equation $y = 3x + 2$. Let's evaluate each point by substituting its coordinates $(x, y)$ into the equation.

The equation is: $y = 3x + 2$

1. For the point $(1, 2)$:

Substitute $x = 1$ into the equation: $y = 3(1) + 2 = 3 + 2 = 5$ Since $y = 5$, but the given point has $y = 2$, this point is not a solution.

2. For the point $(2, 8)$:

Substitute $x = 2$ into the equation: $y = 3(2) + 2 = 6 + 2 = 8$ Since $y = 8$, this point is a solution.

3. For the point $(3, 5)$:

Substitute $x = 3$ into the equation: $y = 3(3) + 2 = 9 + 2 = 11$ Since $y = 11$, but the given point has $y = 5$, this point is not a solution.

4. For the point $(0, 0)$:

Substitute $x = 0$ into the equation: $y = 3(0) + 2 = 0 + 2 = 2$ Since $y = 2$, but the given point has $y = 0$, this point is not a solution.

Conclusion:

The point $(2, 8)$ is the only solution to the equation $y = 3x + 2$.

Would you like any further details or explanations?

Here are five related questions to explore:

1. How can we graphically determine whether a point lies on a line?
2. What is the general method to verify if a point is a solution to a linear equation?
3. How do we interpret the slope and y-intercept in the equation $y = 3x + 2$?
4. Can you find a point that lies on the line $y = 3x + 2$ other than $(2, 8)$?
5. How would you describe the relationship between $x$ and $y$ in the equation $y = 3x + 2$?

Tip: For any linear equation in the form $y = mx + b$, $m$ represents the slope, and $b$ represents the y-intercept. This can help visualize how the graph behaves.