Question

which graph best represents the solution set of $y \leq -4x$? (images of four graphs labeled a, b, c, d are shown)

Explanation:

Step1: Analyze the boundary line

The inequality is \(y\leq - 4x\). The boundary line is \(y=-4x\). Since the inequality is \(\leq\), the boundary line is solid (not dashed).

Step2: Test a point

Test the point \((0,0)\). Substitute \(x = 0\) and \(y = 0\) into \(y\leq - 4x\). We get \(0\leq-4\times0\), which is \(0\leq0\) (a True statement). So the region containing \((0,0)\) should be shaded.

Answer:

C.