Question

y < -4x + 5

Explanation:

1. Graph the boundary line: The equation \(y = - 4x+5\) is in slope - intercept form (\(y=mx + b\), where \(m=-4\) is the slope and \(b = 5\) is the \(y\)-intercept). A dashed line is used because the inequality is strict (\(<\), not \(\leq\)).
2. Test a point for shading: Using the origin \((0,0)\) (a common test point not on the line \(y=-4x + 5\)) helps determine the correct region. Since the test point satisfies the inequality, we shade the region that contains the test point, which is below the dashed line.

Answer:

To graph \( y < -4x + 5 \):

Step1: Graph the boundary line

The boundary line is \( y=-4x + 5 \). It has a slope of \(-4\) and a \(y\)-intercept of \(5\). Plot the \(y\)-intercept \((0,5)\). Then, use the slope to find another point: from \((0,5)\), move down \(4\) units and right \(1\) unit to get \((1,1)\). Since the inequality is \(y < -4x + 5\) (not \(y\leq -4x + 5\)), draw a dashed line through these points.

Step2: Shade the region

To determine which side to shade, test a point not on the line, e.g., \((0,0)\). Substitute into the inequality: \(0 < -4(0)+5\) simplifies to \(0 < 5\), which is true. So, shade the region below the dashed line (where \((0,0)\) lies).