Classify the Linear Function: Understanding y=2-3x

To determine the characteristic of the function $y = 2 - 3x$, we will evaluate the slope:

• The given function is in the form $y = mx + b$, which indicates a linear equation. Here, $y = 2 - 3x$ can be rearranged as $y = -3x + 2$, showing that $m = -3$.
• The slope $m$ is $-3$.
• In a linear function, the sign of the slope $m$ determines the function's behavior:
• If the slope $m$ is positive ($m > 0$), the function is increasing.
• If the slope $m$ is negative ($m < 0$), the function is decreasing.
• If the slope $m = 0$, the function is constant.
• Since $m = -3$, which is negative, we conclude that the function is decreasing.

Therefore, the function described by $y = 2 - 3x$ is decreasing.