1. The problem is to sketch the graph of a linear inequality, which means we need to represent all the points $(x,y)$ that satisfy the inequality. 2. The general form of a linear inequality is $ax + by \leq c$, $ax + by \geq c$, $ax + by < c$, or $ax + by > c$. 3. To graph it, first graph the boundary line $ax + by = c$. This line divides the plane into two half-planes. 4. If the inequality is $\leq$ or $\geq$, the boundary line is solid, meaning points on the line satisfy the inequality. 5. If the inequality is $<$ or $>$, the boundary line is dashed, meaning points on the line do not satisfy the inequality. 6. To determine which side of the line to shade, pick a test point not on the line (usually $(0,0)$ if not on the line) and substitute into the inequality. 7. If the test point satisfies the inequality, shade the side of the line containing the test point; otherwise, shade the opposite side. 8. This shaded region represents all solutions to the inequality. This method applies to any linear inequality you want to graph.