Question

select all the correct answers.

bradley is returning home from a place that is 2 kilometers away. the function \\(y = 2,000 - 90x\\) represents bradleys distance from home in meters, \\(y\\), in relation to the number of minutes he walks, \\(x\\).

which statements about this function are true?

• the function is a linear function.
• the function is a nonlinear function.
• the function does not change at a constant rate.
• the function is an increasing function.
• the function changes at a constant rate.

Explanation:

Analyze the function form

Using the Linear Equations knowledge point

$$ y = -90x + 2000 $$

Determine linearity and rate of change

Using the Linear Equations knowledge point

$$
LATEXBLOCK0
$$

Determine if the function is increasing

Using the Increasing Functions knowledge point

$$ m = -90 < 0 \implies \text{decreasing function} $$

Evaluate the given statements

• "The function is a linear function." (True, fits \(y = mx + b\))
• "The function is a nonlinear function." (False)
• "The function does not change at a constant rate." (False, linear functions have a constant rate of change)
• "The function is an increasing function." (False, the slope is negative)
• "The function changes at a constant rate." (True, the slope is constant at \(-90\))

Answer:

• The function is a linear function. (Correct answer)
• The function is a nonlinear function.
• The function does not change at a constant rate.
• The function is an increasing function.
• The function changes at a constant rate. (Correct answer)