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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.

1 answer

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.