Question

The graph represents the ascent of a plane after takeoff in feet per minute.

A) Does the graph represent a proportional relationship? Explain your reasoning.

B) What is the unit rate of change for this situation?

Answer 1

A) Yes, the graph represents a proportional relationship because the rate at which the plane's altitude increases is directly proportional to the amount of time that has elapsed since takeoff.

B) The unit rate of change is the number of feet per minute that increases over time, which can be calculated by finding the slope of the line. To do this, we choose two arbitrary points on the line and calculate the change in altitude divided by the change in time for each point. Therefore, if we choose the points (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 12000), then the unit rate of change is (12000 - 0) / (2 - 0).

The unit rate of change is 6000 feet per minute, calculated by (12000 - 0) / (2 - 0).

If you have any additional questions or need further assistance, please let me know.

Answer 2

• A) Yes,
• B) 6000 feet/min

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Proportional relationship is:

• y = kx, where k- constant or rate of change.

At x = 0, the function gets the value of zero regardless the value of k. Hence the line passes through the origin.

A) The given graph passes through the origin and therefore it is a proportional relationship.

B) The value of y = k when x = 1 is the rate of change.

As per graph it is:

• x = 1 ⇒ y = 6000 feet/min