Question

The data in which table represents a linear function that has a slope of zero?
A 2-column table with 5 rows. Column 1 is labeled x with entries negative 5, negative 4, negative 3, negative 2, negative 1. Column 2 is labeled y with entries 5, 5, 5, 5, 5.
A 2-column table with 5 rows. Column 1 is labeled x with entries 1, 2, 3, 4, 5. Column 2 is labeled y with entries negative 5, negative 4, negative 3, negative 2, negative 1.
A 2-column table with 5 rows. Column 1 is labeled x with entries negative 5, negative 4, negative 3, negative 2, negative 1. Column 2 is labeled y with entries 5, 4, 3, 2, 1.
A 2-column table with 5 rows. Column 1 is labeled x with entries 5, 5, 5, 5, 5. Column 2 is labeled y with entries negative 5, negative 4, negative 3, negative 2, negative 1.

Answer 1

A linear function with a slope of zero means that the y-value remains constant regardless of the x-value.

Let's analyze the tables provided:

1. **First table:**
- \( x: -5, -4, -3, -2, -1 \)
- \( y: 5, 5, 5, 5, 5 \)
- **Slope = 0** (constant y-value of 5)

2. **Second table:**
- \( x: 1, 2, 3, 4, 5 \)
- \( y: -5, -4, -3, -2, -1 \)
- **Not a slope of 0** (y-values are changing)

3. **Third table:**
- \( x: -5, -4, -3, -2, -1 \)
- \( y: 5, 4, 3, 2, 1 \)
- **Not a slope of 0** (y-values are changing)

4. **Fourth table:**
- \( x: 5, 5, 5, 5, 5 \)
- \( y: -5, -4, -3, -2, -1 \)
- **Not a slope of 0** (y-values are changing)

The table that represents a linear function with a slope of zero is the **first table**, where all y-values are constant at 5.