Mathematical Statement Analysis: Evaluating Truth Values in Given Expressions

To solve this problem, we'll examine the statements related to the slope of a linear function and determine which are true:

• A linear function is described mathematically by the equation $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

• The slope $m$ determines the direction of the line:

  • If $m > 0$, the line is increasing as $x$ increases.

  • If $m = 0$, the line is horizontal, meaning it is constant.

  • If $m < 0$, the line is decreasing as $x$ increases.

Now, let's match these characteristics to the provided choices:

• If the slope is positive, then the function is increasing.

  • This is true as per the description above; a positive slope means the function increases as $x$ increases.

• If the slope is negative, then the function is constant.

  • This is incorrect; a negative slope results in a decreasing function.

• If the slope is positive, then the function is decreasing.

  • This is incorrect; a positive slope corresponds to an increasing function.

• If the slope is negative, then the function is increasing.

  • This is incorrect; a negative slope means the function is decreasing.

Therefore, the correct statement is that If the slope is positive, then the function is increasing.