Question

essay 4 points match each equation to the graph it represents. x = -3 x = 3 y = -3 y = 3

Explanation:

Step1: Recall line - equation properties

The equation \(x = a\) represents a vertical line passing through the point \((a,0)\) on the \(x\) - axis. The equation \(y = b\) represents a horizontal line passing through the point \((0,b)\) on the \(y\) - axis.

Step2: Analyze \(x=-3\)

The equation \(x = - 3\) is a vertical line that passes through the point \((-3,0)\). It is parallel to the \(y\) - axis and 3 units to the left of the \(y\) - axis.

Step3: Analyze \(x = 3\)

The equation \(x = 3\) is a vertical line that passes through the point \((3,0)\). It is parallel to the \(y\) - axis and 3 units to the right of the \(y\) - axis.

Step4: Analyze \(y=-3\)

The equation \(y=-3\) is a horizontal line that passes through the point \((0, - 3)\). It is parallel to the \(x\) - axis and 3 units below the \(x\) - axis.

Step5: Analyze \(y = 3\)

The equation \(y = 3\) is a horizontal line that passes through the point \((0,3)\). It is parallel to the \(x\) - axis and 3 units above the \(x\) - axis.

Answer:

For a vertical line 3 units to the left of the \(y\) - axis: \(x=-3\)
For a vertical line 3 units to the right of the \(y\) - axis: \(x = 3\)
For a horizontal line 3 units below the \(x\) - axis: \(y=-3\)
For a horizontal line 3 units above the \(x\) - axis: \(y = 3\)