Linear Function Through Points (0,0) and (2,0): Finding the Equation

Let's identify the nature of the function given the points $B(0,0)$ and $A(2,0)$.

Step 1: Calculate the slope $m$ of the line using the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.

The coordinates given are $B(0,0)$ and $A(2,0)$. Here, $x_1 = 0$, $y_1 = 0$, $x_2 = 2$, and $y_2 = 0$.

Plug these values into the formula:

$m = \frac{0 - 0}{2 - 0} = \frac{0}{2} = 0$

The slope $m$ is $0$.

Step 2: Write the linear function equation.

Using the equation of a line in slope-intercept form $y = mx + b$, where $m = 0$:

$y = 0x + b$

Since both points $B(0,0)$ and $A(2,0)$ satisfy $y = 0$, the y-intercept $b = 0$.

Thus, the equation of the line is $y = 0$.

This equation represents a constant function, specifically the x-axis, where $y$ remains constant at zero for any $x$.

Therefore, the nature of the function given the points B(0,0) and A(2,0) is a constant function.