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=
Good work!
Now that we know Charlie’s elevation when Charlie starts the climb, substitute the vertical intercept for b 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
=
160x + b
y
=
160x +
b
=
80
Nice!
Let’s use the equation to help us make a prediction. Remember x represents the time in hours, and y represents Charlie’s elevation. What will Charlie’s elevation be after 5 hours? Solve on paper or use the calculator. Then, enter your answer on Zearn.
y
=
160x + 80
y
=
160(5) + 80
y = 800 + 80
y = 880
After 5 hours, Charlie's elevation will be 880 meters.