Question

elevation (feet above sea level)
12,000
11,000
10,000
9,000
8,000
7,000
6,000
5,000
6 12 18 24 30 36 42 48 54 60
minutes on the train
complete the statement that describes the situation.
larry gets on the train at an altitude of feet. his elevation decreases on his way down the mountain.

Explanation:

Step1: Find initial altitude

The x - axis is minutes on the train, and at \( x = 0 \) (when Larry gets on the train), we look at the y - axis (elevation). From the graph, when \( x = 0 \), the elevation is 12,000 feet.

Step2: Calculate rate of decrease (slope)

We can take two points, say \( (0, 12000) \) and \( (60, 5500) \) (approximate from the graph). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5500 - 12000}{60 - 0}=\frac{- 6500}{60}\approx - 108.33 \) feet per minute. But more accurately, looking at the grid, from \( x = 0 \) (12,000) to \( x = 60 \), the elevation goes from 12,000 to around 5,500? Wait, no, let's check the graph again. Wait, the first point is at \( x = 0 \), \( y = 12000 \), and at \( x = 60 \), \( y\approx5500 \)? Wait, no, maybe better to take \( (0,12000) \) and \( (60, 5500) \) is wrong. Wait, looking at the graph, the line starts at (0,12000) and ends at (60, 5500)? Wait, no, the y - axis at 60 minutes: the point is at around 5500? Wait, no, the grid lines: each y - grid is 1000 feet. At x = 60, the elevation is between 5000 and 6000, closer to 5500? Wait, maybe the correct two points are (0,12000) and (60, 5500) is incorrect. Wait, let's see the slope formula. The slope is \( \frac{\Delta y}{\Delta x} \). From x = 0 (12,000) to x = 60, the change in y is \( y_2 - y_1 \), and change in x is 60 - 0 = 60. If we look at the graph, at x = 30, y = 10,000. So using (0,12000) and (30,10000), the slope is \( \frac{10000 - 12000}{30 - 0}=\frac{- 2000}{30}=-\frac{200}{3}\approx - 66.67 \) feet per minute? Wait, no, wait the graph: at x = 0, y = 12,000; at x = 60, y = 5,500? Wait, maybe the first blank is 12,000.

Answer:

Larry gets on the train at an altitude of 12000 feet. (For the second blank, we can calculate the rate: from (0,12000) to (60, 5500) is not right, wait, looking at the graph, when x = 0, y = 12,000; when x = 60, y = 5500? No, maybe the correct points are (0,12000) and (60, 5500) is wrong. Wait, the graph's y - axis: 5000, 6000, 7000, etc. Wait, at x = 60, the elevation is 5500? No, maybe the first blank is 12000. So the first answer is 12000.