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)
0
2
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14
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20
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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
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
b=
20
Therefore, the equation representing this situation is y = 30x + 20. With this equation, we can make a prediction for Johnny's elevation after 10 minutes:
y = 30(10) + 20
y = 300 + 20
y = 320
So, after 10 minutes, Johnny's elevation will be 320 meters.