Question

name the quadrant or axis where each point lies.
(-8, 0):
(choose one)
(-5, 3):
(choose one)
(2, -4):
(choose one)
(-4, -6):
(choose one)

Explanation:

For point \((-8, 0)\):

Step1: Recall axis definitions

A point lies on the \(x\)-axis if its \(y\)-coordinate is \(0\), and on the \(y\)-axis if its \(x\)-coordinate is \(0\). For \((-8, 0)\), the \(y\)-coordinate is \(0\), so it lies on the \(x\)-axis.

Step1: Recall quadrant signs

In Quadrant I: \((+, +)\), Quadrant II: \((-, +)\), Quadrant III: \((-, -)\), Quadrant IV: \((+, -)\). For \((-5, 3)\), \(x = -5\) (negative) and \(y = 3\) (positive), so it matches Quadrant II's sign pattern.

Step1: Recall quadrant signs

For \((2, -4)\), \(x = 2\) (positive) and \(y = -4\) (negative), which matches Quadrant IV's \((+, -)\) pattern.

Answer:

\(x\)-axis

For point \((-5, 3)\):