To solve the problem of drawing the graphs for the given equations, we will follow these steps for each equation:
### Step-by-Step Solution:
1. **Graph of \( y = 3 \)**:
- This equation indicates that for any value of \( x \), \( y \) will always be 3.
- To draw the graph, plot points where \( y = 3 \) for various \( x \) values. For example:
- When \( x = -2 \), \( y = 3 \) → Point (-2, 3)
- When \( x = 0 \), \( y = 3 \) → Point (0, 3)
- When \( x = 2 \), \( y = 3 \) → Point (2, 3)
- Connect these points with a straight horizontal line parallel to the x-axis at \( y = 3 \).
2. **Graph of \( y + 5 = 0 \)**:
- Rearranging gives \( y = -5 \).
- For this equation, \( y \) is always -5 regardless of \( x \).
- Plot points where \( y = -5 \):
- When \( x = -2 \), \( y = -5 \) → Point (-2, -5)
- When \( x = 0 \), \( y = -5 \) → Point (0, -5)
- When \( x = 2 \), \( y = -5 \) → Point (2, -5)
- Draw a horizontal line parallel to the x-axis at \( y = -5 \).
3. **Graph of \( x = 4 \)**:
- This equation indicates that for any value of \( y \), \( x \) will always be 4.
- Plot points where \( x = 4 \):
- When \( y = -2 \), \( x = 4 \) → Point (4, -2)
- When \( y = 0 \), \( x = 4 \) → Point (4, 0)
- When \( y = 2 \), \( x = 4 \) → Point (4, 2)
- Connect these points with a straight vertical line parallel to the y-axis at \( x = 4 \).
4. **Graph of \( x = 6 \)**:
- Similar to the previous equation, \( x \) is always 6 regardless of \( y \).
- Plot points where \( x = 6 \):
- When \( y = -2 \), \( x = 6 \) → Point (6, -2)
- When \( y = 0 \), \( x = 6 \) → Point (6, 0)
- When \( y = 2 \), \( x = 6 \) → Point (6, 2)
- Draw a vertical line parallel to the y-axis at \( x = 6 \).
### Summary of Graphs:
- The graph of \( y = 3 \) is a horizontal line at \( y = 3 \).
- The graph of \( y + 5 = 0 \) is a horizontal line at \( y = -5 \).
- The graph of \( x = 4 \) is a vertical line at \( x = 4 \).
- The graph of \( x = 6 \) is a vertical line at \( x = 6 \).
