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Difficulty: MediumInterpreting Linear Relationships in Context

A commercial drone descends from a mapping mission at a constant rate. The altitude of the drone, AA, in meters, tt seconds after it begins its descent is modeled by the equation A=−4.5t+360A = -4.5t + 360. The graph of this equation in the tAtA-plane is shown below.

Which of the following is the best interpretation of the tt-intercept of the graph in this context?

  1. The number of seconds it takes for the drone to reach sea level.Answer
  2. B
    The altitude, in meters, of the drone when it begins its descent.
  3. C
    The rate, in meters per second, at which the drone descends.
  4. D
    The number of seconds it takes for the drone to descend 1 meter.

Answer

The tt-intercept represents the number of seconds it takes for the drone to reach sea level.
The correct answer is the option stating that the intercept represents the number of seconds it takes for the drone to reach sea level. The tt-intercept is the point on the graph where A=0A = 0. In this context, A=0A = 0 means the drone's altitude is 00 meters (sea level), and tt represents the time elapsed in seconds. Setting A=0A = 0 in the equation A=−4.5t+360A = -4.5t + 360 gives t=80t = 80, meaning it takes 8080 seconds for the drone to reach sea level.

Step-by-Step Solution

1
Identify the meaning of the tt-intercept on the graph.
The tt-intercept is the point on the graph where the vertical coordinate, AA, is equal to 00.
By definition, the horizontal intercept of a function occurs when the dependent variable (altitude, AA) is zero.
2
Relate the condition A=0A = 0 to the context.
An altitude of A=0A = 0 meters corresponds to sea level.
The variable AA represents altitude in meters, so A=0A = 0 represents the level where altitude is zero, which is sea level.
3
Interpret the corresponding value of tt.
The tt-coordinate represents the time, in seconds, when the altitude is 0.
Since tt represents the number of seconds after the descent began, the tt-intercept (80,0)(80, 0) indicates that it takes 8080 seconds for the drone to reach sea level.

Key Concept

Interpreting the intercepts of a linear relationship in context.
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Topics

Interpreting Linear Relationships in Context

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