Question

graph this inequality:
x > -1
plot points on the boundary line. select the line to switch between solid and dotted. select a
region to shade it.

Explanation:

Step1: Identify the boundary line

The inequality is \( x > -1 \). The boundary line for this inequality is \( x = -1 \). Since the inequality is "greater than" (not "greater than or equal to"), the boundary line should be a dotted line. This is because the points on the line \( x = -1 \) do not satisfy the inequality \( x > -1 \).

Step2: Determine the shading region

To determine which region to shade, we can test a point not on the boundary line. A common test point is the origin \((0,0)\). Substitute \( x = 0 \) into the inequality: \( 0 > -1 \), which is true. So, we shade the region to the right of the line \( x = -1 \) (since all points with \( x \)-coordinate greater than -1 will satisfy the inequality).

Step3: Plot the boundary line and shade

• Draw a dotted vertical line at \( x = -1 \) (because the inequality is strict, \( x > -1 \), not \( x\geq -1 \)).
• Shade the area to the right of this dotted line, as all points in this region have \( x \)-values greater than -1, which satisfies the inequality \( x > -1 \).

Answer:

1. Draw a dotted vertical line at \( x = -1 \) (since the inequality is \( x > -1 \), not \( x\geq -1 \), the boundary is not included).
2. Shade the region to the right of the line \( x = -1 \) (all points in this region have \( x \)-coordinates greater than -1, satisfying \( x > -1 \)).