Questions: Write the inequality shown by the shaded region in the graph with the boundary line y=-8x/3-1.

Solution Steps

The boundary line given in the problem is \( y = -\frac{8x}{3} - 1 \).

The shaded region is to the left of the boundary line. This indicates that the inequality will involve \( \leq \) or \( \geq \).

Choose a point in the shaded region to determine the correct inequality. A convenient point is \((0, 0)\).

Substitute \((0, 0)\) into the boundary line equation: \[ 0 \leq -\frac{8(0)}{3} - 1 \] \[ 0 \leq -1 \]

This is false, so the correct inequality is: \[ y \geq -\frac{8x}{3} - 1 \]

Final Answer