Question

y ≥ 4
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 \( y \geq 4 \). The boundary line is \( y = 4 \), which is a horizontal line parallel to the x - axis passing through \( y = 4 \) on the y - axis. Since the inequality is \( \geq \), the line should be solid (because the points on the line are included in the solution set).

Step2: Plot points on the boundary line

We can choose several points on the line \( y = 4 \). For example, when \( x = 0 \), \( y = 4 \) (the point \( (0,4) \)); when \( x = 2 \), \( y = 4 \) (the point \( (2,4) \)); when \( x=- 2 \), \( y = 4 \) (the point \( (-2,4) \)) etc. Plot these points and draw a solid horizontal line through them.

Step3: Determine the region to shade

To determine which region to shade, we can test a point not on the line. Let's take the point \( (0,5) \) (which is above the line \( y = 4 \)). Substitute \( x = 0 \) and \( y = 5 \) into the inequality \( y\geq4 \). We get \( 5\geq4 \), which is true. So we shade the region above the line \( y = 4 \) (including all the points where the y - coordinate is greater than or equal to 4).

Answer:

1. Draw a solid horizontal line \( y = 4 \) (plot points like \( (0,4) \), \( (2,4) \), \( (-2,4) \) etc. on this line).
2. Shade the region above the line \( y = 4 \) (the region where \( y\) - values are 4 or greater).