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I see the image of a math problem related to the elevation of a passenger in a tram ride to Sandia Peak. The question starts by stating that the passenger begins at an elevation of 6,559 feet, and after 1 minute, the passenger is at 6,315 feet.

Here's a breakdown of how to solve the problem:

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### (a) **Find a linear function for the passenger’s elevation, \( h \), in feet, \( t \), minutes after starting the ride.**

To find a linear function, we assume the form \( h(t) = mt + b \), where:
- \( m \) is the slope of the line (the rate of change in elevation per minute),
- \( b \) is the initial elevation (at \( t = 0 \)).

Given:
- Initial elevation: 6,559 feet at \( t = 0 \),
- Elevation after 1 minute: 6,315 feet.

To find the slope \( m \), use the slope formula between two points \( (t_1, h_1) \) and \( (t_2, h_2) \):

\[
m = \frac{h_2 - h_1}{t_2 - t_1}
\]

Substituting the points \( (0, 6559) \) and \( (1, 6315) \):

\[
m = \frac{6315 - 6559}{1 - 0} = \frac{-244}{1} = -244 \text{ feet per minute}
\]

Now, using \( h(0) = 6559 \), the linear equation becomes:

\[
h(t) = -244t + 6559
\]

### (b) **Give the units and practical interpretation of the slope and vertical intercept.**

- **Slope**: The slope is \( -244 \) feet per minute, meaning the passenger's elevation decreases by 244 feet per minute as the tram descends.
- **Vertical intercept**: The vertical intercept is 6,559 feet, which is the starting elevation of the tram at \( t = 0 \).

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Do you need any further clarification or details? 

Here are 5 related questions for practice:
1. What does a positive slope represent in a similar context?
2. How would the equation change if the tram ascended instead of descending?
3. What is the elevation after 5 minutes using the function you found?
4. How can you verify that the slope calculation is correct?
5. If the tram stops after 3 minutes, what is the final elevation?

**Tip:** Always verify linear function parameters (slope and intercept) by checking the provided data points.

A passenger's tram ride to go up to Sandia Peak begins at an elevation of 6559 feet. One minute after starting, the passenger is at 6315 feet.
(a) Find a linear function for the passenger's elevation, h, in feet, t minutes after starting the ride.
(b) Give the units and practical interpretation of the slope and vertical intercept.

This problem involves finding a linear function for a passenger's elevation during a tram ride to Sandia Peak, starting at 6559 feet and decreasing to 6315 feet after one minute. It also interprets the slope and vertical intercept of the linear equation. Suitable for Grades 9-10.

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