You have provided two equations:

1. \( y = 0.5x + 3 \)
2. \( y = -1.5 + 0.5x \)

We can now compare or solve for when these two equations are equal. Let's set them equal to each other to find the values of \(x\) and \(y\):

\[
0.5x + 3 = -1.5 + 0.5x
\]

Now, let's simplify the equation.

### Step 1: Subtract \(0.5x\) from both sides
\[
3 = -1.5
\]

### Conclusion:
This results in a false statement, \( 3 \neq -1.5 \). Therefore, these two lines are **parallel** and do not intersect at any point.

Since the slopes are equal (both are 0.5), the lines are parallel but have different y-intercepts, meaning they will never meet or have any points in common.

Would you like further clarification or a graphical representation of these two lines?

### Related Questions:
1. How do we know when two lines are parallel?
2. What happens when two lines have the same slope but different y-intercepts?
3. How can we check if two lines are identical?
4. What is the condition for two lines to intersect?
5. What changes in the equation if the lines were to intersect?

### Tip:
Parallel lines have identical slopes but different y-intercepts, and they never meet.

Explore how to determine if two lines are parallel using equations. Solve the problem y = 0.5x + 3 and y = -1.5 + 0.5x with detailed steps and explanations. Suitable for high school students studying equations and parallel lines.

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