What is the boundary line of (y\geq -4)?

Correct answer: (y=-4)

The boundary of an inequality is obtained by replacing the inequality sign with an equality sign. For \(y\geq-4\), the boundary equation is \(y=-4\). This is a horizontal line because the y-coordinate remains fixed at -4 while x can have any value. The boundary divides the coordinate plane into points above it and points below it.

Since the original sign is \(\geq\), the boundary itself is included, and the solution region consists of the points on or above the line \(y=-4\). For example, \((0,0)\) satisfies \(0\geq-4\), while \((0,-5)\) does not. Thus option B gives the boundary line. The equations involving x or both variables describe different lines and cannot be the boundary of this inequality.