This graph represents the linear relationship between the time in hours and Thomas's elevation in meters. For each hour, his elevation increases at a constant rate. After 3 hours, Thomas’s elevation is 1,600 meters. After 7 hours, his elevation is 3,600 meters. Let’s write an equation to represent this line in the form y=mx+b. Start by finding m, or the slope. What is the slope of this line? In other words, what is Thomas’s change in elevation for each hour?

Question

x
y
(3, 1,600)(7, 3,600)
0
1
2
3
4
5
6
7
8
9
10
0
400
800
1,200
1,600
2,000
2,400
2,800
3,200
3,600
4,000
4,400
Time (hours)
Elevation (meters)
y= mx + b

Slope =

Answer 1

To find the slope \( m \) of the line representing Thomas's change in elevation over time, we can use the two points provided:

• Point 1: \( (3, 1600) \)
• Point 2: \( (7, 3600) \)

The formula for the slope \( m \) is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Here, \( (x_1, y_1) = (3, 1600) \) and \( (x_2, y_2) = (7, 3600) \). Plugging in the values, we get:

\[ m = \frac{3600 - 1600}{7 - 3} = \frac{2000}{4} = 500 \]

So the slope \( m \) is 500 meters per hour.

This means Thomas's elevation increases by 500 meters for each hour.

Final answer: Slope = 500