1. The problem is to graph the inequality $3x - y \leq 4$. 2. First, rewrite the inequality to express $y$ in terms of $x$: $$3x - y \leq 4 \implies -y \leq 4 - 3x \implies y \geq 3x - 4.$$ 3. This means the graph is the region above or on the line $y = 3x - 4$. 4. To graph the boundary line, find two points: - When $x = 0$, $y = 3(0) - 4 = -4$. - When $x = 1$, $y = 3(1) - 4 = -1$. 5. Draw the line passing through $(0,-4)$ and $(1,-1)$. 6. Because the inequality is $\geq$, the region above this line (including it) is shaded. Final answer: The graph is the half-plane above and including the line $y = 3x - 4$.