Question

Determine the slope and y-intercept of the linear function represented by the following scenario:

An airplane starts it’s descent at an altitude (height) of 30,000 ft and descends at a rate of 2000 feet per minute.

Answer 1

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.

1. **Y-Intercept**: The y-intercept occurs when \( x = 0 \) (at the start of the descent). The altitude is 30,000 feet, so:
\[
y\text{-intercept} = 30,000
\]

2. **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 \(30,000\).