Are the graphs of each pair of equations parallel, perpendicular, or neither? y = 1/2 y = -3

To determine whether the graphs of the given equations are parallel, perpendicular, or neither, we need to analyze their slopes.

### Given Equations:
1. \( y = \frac{1}{2} \)
2. \( y = -3 \)

#### Step 1: Understanding the nature of these equations
Both of these equations are horizontal lines because they are in the form \( y = c \), where \( c \) is a constant. A horizontal line has a slope of 0.

- **First equation** \( y = \frac{1}{2} \): This represents a horizontal line at \( y = \frac{1}{2} \) with a slope of 0.
- **Second equation** \( y = -3 \): This also represents a horizontal line, but at \( y = -3 \), and it also has a slope of 0.

#### Step 2: Determining the relationship
Since both lines have the same slope (0), they are **parallel** to each other.

### Conclusion:
The graphs of the equations \( y = \frac{1}{2} \) and \( y = -3 \) are **parallel**.

Would you like any further explanation or examples on this topic?

Here are 5 related questions you might find interesting:
1. What is the slope of a vertical line?
2. How do you find the slope between two points on a line?
3. Can two perpendicular lines have the same slope?
4. How do you determine if two lines are perpendicular?
5. What is the general form of a linear equation in slope-intercept form?

**Tip:** Parallel lines always have the same slope but different y-intercepts!

Explore whether the graphs of the equations y = 1/2 and y = -3 are parallel, perpendicular, or neither. This problem covers key concepts like the slope of horizontal lines and how parallel lines share the same slope. Ideal for students in Grades 7-9.

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