Linear Function Graph: Finding Line Through Points (1,5) and (7,1)

To solve this problem, we'll follow these steps:

• Step 1: Identify the given points $B(1, 5)$ and $A(7, 1)$.
• Step 2: Calculate the slope using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.
• Step 3: Interpret the result to determine if the function is increasing, decreasing, or constant.

Now, let's work through each step:
Step 1: The given points are $B(1, 5)$ and $A(7, 1)$.
Step 2: We calculate the slope as follows: $m = \frac{1 - 5}{7 - 1} = \frac{-4}{6} = -\frac{2}{3}$ Step 3: The slope $m = -\frac{2}{3}$ is negative, indicating that the function decreases as $x$ increases.

Therefore, since the slope is negative, the function is a decreasing function.

The correct choice is the first option: Decreasing function.