Angela starts rock climbing at an elevation above sea level. She 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 Angela's elevation in meters. For each hour, her elevation increases at a constant rate. After 2 hours, Angela’s elevation is 630 meters. After 5 hours, her elevation is 1,530 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 Angela’s change in elevation for each hour?
x
y
(2, 630)(5, 1,530)
0
1
2
3
4
5
6
7
8
9
10
11
12
0
180
360
540
720
900
1,080
1,260
1,440
1,620
1,800
1,980
2,160
2,340
2,520
2,700
Time (hours)
Elevation (meters)
y= mx + b
Slope =
You got it!
To represent the relationship between time and Angela’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, 630)(5, 1,530)
0
1
2
3
4
5
6
7
8
9
10
11
12
0
180
360
540
720
900
1,080
1,260
1,440
1,620
1,800
1,980
2,160
2,340
2,520
2,700
Time (hours)
Elevation (meters)
y= mx + b
y=
x+b
Slope = 300
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, 630)(5, 1,530)
0
1
2
3
4
5
6
7
8
9
10
11
12
0
180
360
540
720
900
1,080
1,260
1,440
1,620
1,800
1,980
2,160
2,340
2,520
2,700
Time (hours)
Elevation (meters)
y=300x+b
b=
Nice!
Now that we know Angela’s elevation when Angela starts the climb, substitute the vertical intercept for b in our equation.
x
y
(2, 630)(5, 1,530)
0
1
2
3
4
5
6
7
8
9
10
11
12
0
180
360
540
720
900
1,080
1,260
1,440
1,620
1,800
1,980
2,160
2,340
2,520
2,700
Time (hours)
Elevation (meters)
y
=
300x + b
y
=
300x +
b
=
30
Excellent!
Let’s use the equation to help us make a prediction. Remember x represents the time in hours, and y represents Angela’s elevation. What will Angela’s elevation be after 8 hours? Solve on paper or use the calculator. Then, enter your answer on Zearn.
y
=
300x + 30
y
=
300(8) + 30
y = 2460
After 8 hours, Angela's elevation will be 2,460 meters.