This graph represents the linear relationship between the time in hours and Eddie's elevation in meters. For each hour, his elevation increases at a constant rate. After 2 hours, Eddie’s elevation is 400 meters. After 4 hours, his elevation is 720 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 Eddie’s change in elevation for each hour?

Question

x
y
(2, 400)(4, 720)
0
1
2
3
4
5
6
7
0
80
160
240
320
400
480
560
640
720
800
880
960
1,040
1,120
1,200
1,280
1,360
Time (hours)
Elevation (meters)
y= mx + b

Slope =

Answer 1

To find the slope \( m \) of the linear relationship between time in hours (x) and Eddie's elevation in meters (y), we can use the formula for slope between two points:

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

Given the points \( (2, 400) \) and \( (4, 720) \):

• \( x_1 = 2 \)
• \( y_1 = 400 \)
• \( x_2 = 4 \)
• \( y_2 = 720 \)

We can substitute these values into the slope formula:

\[ m = \frac{720 - 400}{4 - 2} = \frac{320}{2} = 160 \]

So, the slope \( m \) is 160. This means Eddie’s change in elevation for each hour is 160 meters.

Now we can write down the slope:

Slope = 160