Is the Linear Function y = x - 1 Increasing or Decreasing?

To determine if the function $y = x - 1$ is increasing or decreasing, we will analyze its slope:

• Step 1: Identify the function as a linear function in the form $y = mx + b$ where $m = 1$ and $b = -1$.

• Step 2: Recall that for a linear function, if the slope m > 0 , the function is increasing. Conversely, if m < 0 , it is decreasing.

• Step 3: Calculate the slope: $m = 1$. Since $m = 1$ is positive, this means the function is increasing.

The behavior of the function depends on the sign of the slope. Here, because the slope is positive, the function $y = x - 1$ increases as $x$ increases across its entire domain.

Therefore, the function is Increasing.