Question

Charlie starts rock climbing at an elevation above sea level. He climbs up at a constant rate per hour. Write an equation to represent this situation. Then use the equation to make a prediction.
This graph represents the linear relationship between the time in hours and Charlie's elevation in meters. For each hour, his elevation increases at a constant rate. After 2 hours, Charlie’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 Charlie’s change in elevation for each hour?
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 =
Great job!
To represent the relationship between time and Charlie’s elevation, a linear equation can be written in the form y=mx+b. Substitute the slope for m in our equation.
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
y=
x+b

Slope = 160
Excellent!
Now, solve for b, or the vertical intercept. You can can substitute the x and y-values for a point on the line into the equation to help you. Solve on paper or use the calculator. Then, enter your answer on Zearn.
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=160x+b

b=

Answer 1

80

Now, we have the equation representing Charlie's rock climbing situation:

Elevation = 160x + 80

To make a prediction, let's plug in x = 6, representing 6 hours of climbing:

Elevation = 160(6) + 80
Elevation = 960 + 80
Elevation = 1040 meters

Therefore, after 6 hours of climbing, Charlie's elevation will be 1040 meters.