Linear Function Through Points (0,0) and (4,6): Graph Analysis

To determine the type of linear function represented by a line passing through the points $B(0,0)$ and $A(4,6)$, we follow these steps:

• Step 1: Identify the points. Here, we have $B(0,0)$ and $A(4,6)$.
• Step 2: Use the slope formula to find the slope of the line. The formula to find the slope $m$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Plug in the coordinates of the points:

$m = \frac{6 - 0}{4 - 0} = \frac{6}{4} = \frac{3}{2}$.

• Step 3: Analyze the slope: Since the slope $m = \frac{3}{2}$ is positive, the function is an increasing function.
• Step 4: Determine the type of function: A positive slope indicates that the function is increasing as we move from left to right on the graph.

Therefore, the correct description of this linear function, based on the given options, is a Bottom-up function.