Betsy starts hiking at an elevation above sea level. She 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 Betsy's elevation in meters. For each minute, her elevation increases at a constant rate. After 4 minutes, Betsy’s elevation is 140 meters. After 8 minutes, her 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 Betsy’s change in elevation for each minute?
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y
(4, 140)(8, 260)
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Elevation (meters)
y= mx + b
Slope =
Good work!
To represent the relationship between time and Betsy’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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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)
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Time (minutes)
Elevation (meters)
y=30x+b
b=
50
Therefore, the equation representing this situation is y = 30x + 50.
To make a prediction, we can plug in any value for x (time in minutes) into the equation to find the corresponding y value (elevation in meters).
For example, if we plug in x = 10, we get y = 30(10) + 50 = 300 + 50 = 350.
So, after 10 minutes, Betsy's elevation would be 350 meters above sea level.