1. **State the problem:** We are given the function $f(x) = 2x - 6$ and asked to find the slope (rate of change) of this function. 2. **Recall the formula:** For a linear function of the form $f(x) = mx + b$, the slope (rate of change) is the coefficient $m$ of $x$. 3. **Identify the slope:** In $f(x) = 2x - 6$, the coefficient of $x$ is 2. 4. **Interpretation:** This means for every 1 unit increase in $x$, $f(x)$ increases by 2 units. 5. **Sketching the graph:** The graph is a straight line with slope 2 and y-intercept at $-6$. **Final answer:** The slope (rate of change) of the function $f(x) = 2x - 6$ is $2$.