Can a Decreasing Function Connect These Two Points? Graph Challenge

To determine if a decreasing function is possible with the two given points, we need to calculate the slope between them based on the common definition of a decreasing function.

Let's follow these steps:

• Step 1: Identify the given points.
• Step 2: Calculate the slope using these points.
• Step 3: Verify that the slope is negative.

Step 1: The points appear to be roughly at coordinates near $(x_1, y_1)$ and $(x_2, y_2)$ according to their positions on the graph, with exact coordinates not provided, we'll assume accurate readings from the visual information.

Step 2: Calculate the slope using the formula:

$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$

Given the visual interpretation:

$x_1 < x_2$ and $y_1 > y_2$, so this ensures the change in $y$ is negative when divided by a positive change in $x$.

Step 3: As the slope $\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$ is negative, the function represented by these points is decreasing.

Therefore, it is POSSIBLE to generate a decreasing function with the two given points.