What characteristic is associated with a decreasing linear function?

What characteristic is associated with a decreasing linear function?

• A. Positive gradient
• B. Negative gradient
• C. Constant value
• D. Exponential growth

Answer: (B)

A decreasing linear function is characterized by a negative gradient, which indicates that as the independent variable increases, the dependent variable decreases. The gradient, or slope of the line, gives us an idea of how quickly the function is decreasing. When this slope is negative, it shows a consistent decrease, meaning for each unit increase in the x-value, the y-value decreases by a fixed amount. The other characteristics mentioned do not apply to a decreasing linear function. A positive gradient, for example, signifies an increasing function where the y-values rise as x increases. A constant value pertains to a horizontal line, where there is no change in y regardless of x, indicating neither increase nor decrease. Lastly, exponential growth involves a function that increases rapidly as x increases and is not linear, meaning it cannot describe the behavior of a linear function, whether it’s increasing or decreasing.

A decreasing linear function is characterized by a negative gradient, which indicates that as the independent variable increases, the dependent variable decreases. The gradient, or slope of the line, gives us an idea of how quickly the function is decreasing. When this slope is negative, it shows a consistent decrease, meaning for each unit increase in the x-value, the y-value decreases by a fixed amount.

The other characteristics mentioned do not apply to a decreasing linear function. A positive gradient, for example, signifies an increasing function where the y-values rise as x increases. A constant value pertains to a horizontal line, where there is no change in y regardless of x, indicating neither increase nor decrease. Lastly, exponential growth involves a function that increases rapidly as x increases and is not linear, meaning it cannot describe the behavior of a linear function, whether it’s increasing or decreasing.