Understanding the connection between the slope to the increase or decrease of the function

Choose the correct answer

To solve this problem, we need to analyze the behavior of a linear function when subject to various slope conditions.

We'll use the slope-intercept form of a line: $y = mx + b$, where $m$ denotes the slope:

• If $m = 0$: The equation becomes $y = b$. This equation describes a horizontal line that does not change as $x$ changes. Thus, the function is constant, matching choice 2.
• If $m > 0$: The line increases as $x$ increases, implying the function is increasing. This is not directly related to the condition of $m = 0$.
• If $m < 0$: The line decreases as $x$ increases, implying the function is decreasing. This is also not directly related to the condition of $m = 0$.

Choice 2 states that "If the slope is zero, then the function is constant." This is the correct statement because a zero slope indicates a horizontal line with no change in value of $y$ as the independent variable $x$ changes.

Therefore, the correct choice is: Choice 2: If the slope is zero, then the function is constant.