1. **State the problem:** Solve the linear inequality $$y \leq 2x - 6$$. 2. **Understand the inequality:** This inequality means that the value of $y$ is less than or equal to the value of the expression $2x - 6$ for any $x$. 3. **Graphical interpretation:** The boundary line is given by the equation $$y = 2x - 6$$. 4. **Plot the boundary line:** This line has a slope of 2 and a y-intercept at -6. 5. **Determine the region:** Since the inequality is $$y \leq 2x - 6$$, the solution includes all points on the line and below it. 6. **Check a test point:** For example, at $x=0$, the boundary line gives $y = 2(0) - 6 = -6$. The inequality says $y \leq -6$. If we test $y = -7$, then $-7 \leq -6$ is true, so the region below the line is the solution. **Final answer:** The solution to the inequality $$y \leq 2x - 6$$ is all points $(x,y)$ on or below the line $$y = 2x - 6$$.