Questions: Graph the inequality. y ≤ -x - 4

Solution Steps

The inequality is \(y \leq -x - 4\). The equation of the boundary line is \(y = -x - 4\).

The equation of the boundary line is \(y = -x - 4\). We can graph this line by finding two points on the line. When \(x = 0\), \(y = -0 - 4 = -4\). So the point \((0, -4)\) is on the line. When \(x = -4\), \(y = -(-4) - 4 = 4 - 4 = 0\). So the point \((-4, 0)\) is on the line. Plot the points \((0, -4)\) and \((-4, 0)\) and draw a solid line through them. The line is solid because the inequality is \(\leq\), which means the points on the line are included in the solution.

Choose a test point not on the line. A good test point is \((0, 0)\).

Substitute the test point \((0, 0)\) into the inequality: \(0 \leq -0 - 4\) \(0 \leq -4\) This is false.

Since the test point \((0, 0)\) does not satisfy the inequality, shade the region that does not contain the test point. This is the region below the line \(y = -x - 4\).

Final Answer The graph of the inequality \(y \leq -x - 4\) is the region below and including the line \(y = -x - 4\).