To find the equations for runways B and C based on the specifications given about their relationships with runway A, we need to analyze the slopes.
-
Finding the slope of runway A:
- The phrase "runway B is to be parallel to runway A" indicates that it will have the same slope as runway A.
- The phrase "runway C is to be perpendicular to runway A" indicates that its slope will be the negative reciprocal of the slope of runway A.
-
Analyzing the provided equations and finding their slopes:
- A. \( y = -\frac{3}{4}x - 4 \) → Slope = \(-\frac{3}{4}\)
- B. \( y = \frac{4}{3}x - 4 \) → Slope = \(\frac{4}{3}\) (negative reciprocal of \(-\frac{3}{4}\))
- C. \( y = -\frac{4}{3}x - 4 \) → Slope = \(-\frac{4}{3}\)
- D. \( y = \frac{3}{4}x - 4 \) → Slope = \(\frac{3}{4}\) (negative reciprocal of \(-\frac{4}{3}\))
-
Determine which equations fit the criteria for either runway B (parallel) or runway C (perpendicular):
-
From equation A, if we take the slope \(-\frac{3}{4}\):
- For runway B (parallel), we need to keep the slope \(-\frac{3}{4}\). Thus, equation A is a possibility.
- For runway C (perpendicular), we would need a slope of \(\frac{4}{3}\), which corresponds to option B.
-
If using equation A's slope \(-\frac{4}{3}\):
- For runway B (parallel), we would need a slope of \(-\frac{4}{3}\), which corresponds to option C.
- For runway C (perpendicular), the slope would be \(\frac{3}{4}\), which corresponds to option D.
-
-
Summary of the slopes:
-
If runway A has a slope of \(-\frac{3}{4}\), then:
- Runway B can be represented by A (same slope: A).
- Runway C can be represented by B (perpendicular: B).
-
If runway A has a slope of \(-\frac{4}{3}\), then:
- Runway B can be represented by C (same slope: C).
- Runway C can be represented by D (perpendicular: D).
-
-
Conclusion: Therefore, the equations that could describe either runway B or C are:
- A. \( y = -\frac{3}{4}x - 4 \) (can be runway A itself).
- B. \( y = \frac{4}{3}x - 4 \) (perpendicular to A if A was with slope \(-\frac{3}{4}\)).
- C. \( y = -\frac{4}{3}x - 4 \) (can serve as runway A with a slope of \(-\frac{4}{3}\)).
- D. \( y = \frac{3}{4}x - 4 \) (perpendicular to A if A had slope \(-\frac{4}{3}\)).
Thus, the correct choices are:
- A
- B
- C
- D
All options can describe either runway B or C depending on the slope of runway A being considered.
1 answer