Question

y ≥ 5
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 \( y \geq 5 \). The boundary line is \( y = 5 \), which is a horizontal line parallel to the x - axis passing through \( y = 5 \) on the y - axis. Since the inequality is "greater than or equal to", the line should be solid.

Step2: Plot points on the boundary line

For the line \( y = 5 \), we can choose any x - value, and the y - value will be 5. For example, when \( x = 0 \), the point is \( (0,5) \); when \( x = 2 \), the point is \( (2,5) \); when \( x=- 2 \), the point is \( (-2,5) \). We can plot these points (or any other points with \( y = 5 \)) on the graph.

Step3: Shade the region

Since the inequality is \( y\geq5 \), we need to shade the region above the line \( y = 5 \) (including the line itself). All the points with \( y \)-coordinate greater than or equal to 5 satisfy the inequality.

To plot the boundary line:

1. Draw a solid horizontal line through \( y = 5 \) (passing through points like \( (0,5) \), \( (2,5) \), \( (- 2,5) \) etc.).
2. Shade the area above this line (where \( y\geq5 \)).

(Note: Since this is a graphing task, the final answer is the graph with the solid line \( y = 5 \) and the region above it shaded. If we were to describe the key elements: the boundary line is \( y = 5 \) (solid), and the shaded region is \( y\geq5 \).)

Answer:

The boundary line is the solid horizontal line \( y = 5 \), and the region above this line (including the line) is shaded to represent \( y\geq5 \).