Question

graph this inequality:
x > -3
plot points on the boundary line. select the line to switch between solid and dotted. select a region to shade it.

Explanation:

Step1: Identify boundary line type

The inequality is \( x > -3 \). Since the inequality is strict (\(>\), not \(\geq\)), the boundary line \( x = -3 \) should be dotted (to show that points on \( x = -3 \) are not included in the solution).

Step2: Draw the boundary line

On the coordinate plane, \( x = -3 \) is a vertical line passing through \( x = -3 \) (i.e., the point \((-3, y)\) for any \( y \)). Plot this vertical line as dotted.

Step3: Determine the shaded region

For the inequality \( x > -3 \), we shade the region where \( x \)-values are greater than \(-3\). This is the region to the right of the dotted line \( x = -3 \).

To graph \( x > -3 \):

1. Draw a dotted vertical line at \( x = -3 \) (since \( x = -3 \) is not part of the solution, as the inequality is \( > \), not \( \geq \)).
2. Shade the region to the right of this dotted line (all points where \( x \)-coordinate is greater than \(-3\), regardless of \( y \)-value).

(Note: To plot the boundary line, mark points like \((-3, 0)\), \((-3, 2)\), \((-3, -2)\), etc., and connect them with a dotted line. Then shade the area to the right of this line.)

Answer:

• Boundary line: Dotted vertical line at \( x = -3 \).
• Shaded region: Area to the right of \( x = -3 \).