Kevin 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 Kevin's elevation in meters. For each hour, his elevation increases at a constant rate. After 2 hours, Kevin’s elevation is 525 meters. After 4 hours, his elevation is 975 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 Kevin’s change in elevation for each hour?
x
y
(2, 525)(4, 975)
0
1
2
3
4
5
6
7
0
75
150
225
300
375
450
525
600
675
750
825
900
975
1,050
1,125
1,200
1,275
1,350
1,425
Time (hours)
Elevation (meters)
y= mx + b
Slope =
Great job!
To represent the relationship between time and Kevin’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, 525)(4, 975)
0
1
2
3
4
5
6
7
0
75
150
225
300
375
450
525
600
675
750
825
900
975
1,050
1,125
1,200
1,275
1,350
1,425
Time (hours)
Elevation (meters)
y= mx + b
y=
x+b
Slope = 225
Good work!
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, 525)(4, 975)
0
1
2
3
4
5
6
7
0
75
150
225
300
375
450
525
600
675
750
825
900
975
1,050
1,125
1,200
1,275
1,350
1,425
Time (hours)
Elevation (meters)
y=225x+b
b=
75
The equation representing Kevin's elevation as he climbs is y=225x+75.
Now, if we want to predict Kevin’s elevation after 6 hours, we can substitute x=6 into the equation:
y= 225(6) + 75
y= 1350 + 75
y= 1425
Therefore, Kevin's elevation after 6 hours is predicted to be 1425 meters.