Question

graph this inequality: y ≥ -7 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 \( y \geq -7 \). The boundary line for this inequality is \( y = -7 \), which is a horizontal line. Since the inequality is "greater than or equal to", the boundary line should be solid (because the points on the line are included in the solution set).

Step2: Plot the boundary line

To plot \( y = -7 \), find the line where the \( y \)-coordinate is always -7. This is a horizontal line passing through \( (0, -7) \), \( (1, -7) \), \( (-1, -7) \), etc. Draw this line as a solid line on the coordinate plane.

Step3: Determine the region to shade

We need to shade the region where \( y \geq -7 \). This means we shade the area above (or on) the line \( y = -7 \). To confirm, we can pick a test point not on the line, say \( (0, 0) \). Substitute into the inequality: \( 0 \geq -7 \), which is true. So the region containing \( (0, 0) \) (the region above \( y = -7 \)) is the solution region. Shade this area.

Answer:

1. Draw a solid horizontal line \( y = -7 \) (passing through points like \( (0, -7) \), \( (2, -7) \), \( (-3, -7) \), etc.).
2. Shade the region above (and including) the line \( y = -7 \).