Linear Function Graph Through Points (4,7) and (7,2)

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

• Step 1: Calculate the slope using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.
  Given points are $B(4,7)$ and $A(7,2)$. Therefore, $x_1 = 4$, $y_1 = 7$, $x_2 = 7$, $y_2 = 2$.
• Step 2: Substitute the values into the formula:
  $m = \frac{2 - 7}{7 - 4} = \frac{-5}{3} = -\frac{5}{3}$.
• Step 3: Determine the nature of the function based on the slope:
  Since $m = -\frac{5}{3}$ is negative, the function is a decreasing function.

Therefore, based on the slope being negative, the function represented by the line passing through these points is a Decreasing function.