To determine the slope and y-intercept of the linear function representing the airplane's descent, we need to express the relationship between time and altitude in a linear form.
Let:
- \( y \) represent the altitude of the airplane (in feet)
- \( x \) represent the time (in minutes)
Given the information:
- The airplane starts at an altitude of 30,000 feet. This gives us the y-intercept of the function.
- The airplane descends at a rate of 2,000 feet per minute. This gives us the slope of the function.
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Y-Intercept: The y-intercept occurs when \( x = 0 \) (at the start of the descent). The altitude is 30,000 feet, so: \[ y\text{-intercept} = 30,000 \]
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Slope: The slope represents the rate of change of altitude with respect to time. Since the airplane is descending at 2,000 feet per minute, this is a negative slope: \[ \text{slope} = -2,000 \]
Combining these, the linear function can be written as: \[ y = -2000x + 30000 \]
Conclusion:
- The slope is \(-2,000\).
- The y-intercept is \(30,000\).