Question

A line passes through (5, –4) and (–1, –4).

Use the work below.

m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction. M = StartFraction negative 4 minus (negative 4) Over negative 1 minus 5 EndFraction. M = StartFraction 0 Over negative 6 EndFraction. M = 0.

What can you conclude about this line? Select all that apply.
It is a vertical line.
It is a horizontal line.
The equation is x = –4.
The equation is y = –4.
It is impossible to have m = 0.

Answer 1

To analyze the line passing through the points (5, -4) and (-1, -4), let’s consider the slope \( m \) that was calculated in the work provided.

### Given Work:
1. \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
2. For \( (5, -4) \) (point 1) and \( (-1, -4) \) (point 2):
\[
m = \frac{-4 - (-4)}{-1 - 5} = \frac{0}{-6} = 0
\]

### Conclusion:
- The slope \( m = 0 \) indicates that the line is horizontal.

- Since both points have the same y-coordinate (-4), the line remains at \( y = -4 \) across all values of \( x \).

### Final Conclusions:
- **It is a horizontal line.** (True)
- **The equation is y = -4.** (True)
- **It is NOT a vertical line.** (False)
- **The equation is NOT x = -4.** (False)
- **It is NOT impossible to have m = 0.** (False)

### Selected Answers:
- It is a horizontal line.
- The equation is y = -4.