Johnny starts hiking at an elevation above sea level. He hikes up at a constant rate per minute. 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 minutes and Johnny's elevation in meters. For each minute, his elevation increases at a constant rate. After 4 minutes, Johnny’s elevation is 140 meters. After 8 minutes, his elevation is 260 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 Johnny’s change in elevation for each minute?
x
y
(4, 140)(8, 260)
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Time (minutes)
Elevation (meters)
y= mx + b
Slope =
Nice!
To represent the relationship between time and Johnny’s elevation, a linear equation can be written in the form y=mx+b. Substitute the slope for m in our equation.
x
y
(4, 140)(8, 260)
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14
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Time (minutes)
Elevation (meters)
y= mx + b
y=
x+b
Slope = 30
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
(4, 140)(8, 260)
0
2
4
6
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14
0
20
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Time (minutes)
Elevation (meters)
y=30x+b
b=
Great job!
Now that we know Johnny’s elevation when Johnny starts the hike, substitute the vertical intercept for b in our equation.
x
y
(4, 140)(8, 260)
0
2
4
6
8
10
12
14
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
400
Time (minutes)
Elevation (meters)
y
=
30x + b
y
=
30x +
b
=
20
Excellent!
Let’s use the equation to help us make a prediction. Remember x represents the time in minutes, and y represents Johnny’s elevation. What will Johnny’s elevation be after 10 minutes? Solve on paper or use the calculator. Then, enter your answer on Zearn.
y
=
30x + 20
y
=
30(10) + 20 = 320
After 10 minutes, Johnny's elevation will be 320 meters.