To determine the correct equation that best represents the floor number of an elevator descending at a steady rate, we need to analyze the given options.
1. Understand the concept:
- When an elevator is descending, it is moving downwards, meaning the floor number is decreasing over time.
- A decreasing floor number over time implies that the slope of the equation must be negative.
2. Examine the slopes:
- Option A: [tex]\( y = -2x + 75 \)[/tex] – The slope here is [tex]\(-2\)[/tex].
- Option B: [tex]\( y = 2x + 75 \)[/tex] – The slope here is [tex]\(2\)[/tex].
- Option C: [tex]\( y = -2x - 75 \)[/tex] – The slope here is [tex]\(-2\)[/tex].
- Option D: [tex]\( y = 2x - 75 \)[/tex] – The slope here is [tex]\(2\)[/tex].
Since we are looking for a negative slope to represent a descending elevator, we can eliminate Options B and D because their slopes are positive.
3. Examine the y-intercept:
- The y-intercept represents the starting floor number of the elevator when [tex]\(x = 0\)[/tex] (at time zero).
- Generally, we assume the elevator starts descending from a higher floor number, so the y-intercept should be positive.
- Option A: [tex]\( y = -2x + 75 \)[/tex] – The y-intercept here is [tex]\(75\)[/tex], which is positive.
- Option C: [tex]\( y = -2x - 75 \)[/tex] – The y-intercept here is [tex]\(-75\)[/tex], which is negative.
Since we are looking for a positive y-intercept to represent starting at a higher floor, we eliminate Option C.
Hence, the correct equation that best represents the floor number of an elevator descending at a steady rate is:
A. [tex]\( y = -2x + 75 \)[/tex]
