Question

1. the equation for the boundary of the inequality graphed is ( y = 3x - 1 ). (lesson 5-5)

write the inequality that represents the graph.

Explanation:

Step1: Analyze the boundary line

The boundary line is \( y = 3x - 1 \). Since the line is solid (not dashed), the inequality will include equality, so we use \( \geq \) or \( \leq \).

Step2: Determine the inequality direction

The shaded region is above the line \( y = 3x - 1 \). For a linear inequality, if the shaded region is above the line \( y = mx + b \), the inequality is \( y \geq mx + b \) (when the line is solid). So substituting \( m = 3 \) and \( b = -1 \), we get \( y \geq 3x - 1 \).

Answer:

\( y \geq 3x - 1 \)