Understanding the Slope of a Linear Function

What is the slope of the linear function representing Mr. Allen's rate of descent as he jumps off a cliff?

Final answer: The slope of the linear function representing Mr. Allen's rate of descent as he jumps off a cliff is -30. Explanation: The slope of the linear function representing the rate of descent of Mr. Allen when he jumps off a cliff is equal to the rate of change of his altitude over time. Since he is descending at a rate of 30 feet per second, the slope of the function would be -30. The negative sign indicates that the altitude is decreasing over time. Thus, the correct choice is A) -30.

Understanding Slope of a Linear Function

Slope is a measure of how two variables change in relation to each other. In the context of a linear function that represents the relationship between two variables, the slope determines how one variable changes with respect to the other.

The slope of a linear function can be calculated by finding the ratio of the change in the dependent variable to the change in the independent variable. In this case, the dependent variable is Mr. Allen's altitude as he jumps off the cliff, and the independent variable is time.

Since Mr. Allen's rate of descent is 30 ft/s, this indicates that for every second that passes, his altitude decreases by 30 feet. This relationship can be graphed as a linear function, where the slope represents the rate of change of altitude with respect to time.

In the given scenario, the slope of the linear function is -30. The negative sign signifies that Mr. Allen's altitude is decreasing, as he descends down the cliff. Therefore, the correct answer to the question about the slope of the linear function representing his rate of descent is A) -30.

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