Questions: Graph the inequality on the axes below. y > -x - 3

Solution Steps

First, we need to graph the boundary line \(y = -x - 3\). We can find two points on this line by choosing arbitrary \(x\) values and solving for \(y\). If \(x = 0\), then \(y = -0 - 3 = -3\). So, \((0, -3)\) is a point on the line. If \(x = -3\), then \(y = -(-3) - 3 = 3 - 3 = 0\). So, \((-3, 0)\) is a point on the line. Plot these two points and draw a dashed line through them since the inequality is \(>\) and not \(\geq\).

Choose a test point not on the line, such as \((0,0)\). Substitute the coordinates into the inequality: \(0 > -0 - 3\) \(0 > -3\) Since this is true, we shade the side of the line containing \((0,0)\).

Final Answer