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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.

Which of the following points is a solution to the equation y = 3x + 2?

Determine which of the following points is a solution to the equation y = 3x + 2. Learn the step-by-step process to check if points satisfy a linear equation. Suitable for Grades 7-9 students.

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