Question

graph this inequality:
$y \geq 5$
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 \( y = 5 \). Since the inequality is "greater than or equal to", the boundary line should be solid (because the points on the line \( y = 5 \) are included in the solution set).

Step2: Plot points on the boundary line

For the line \( y = 5 \), we can choose any x - values. For example, when \( x = 0 \), \( y = 5 \) (the point \( (0,5) \)); when \( x = 2 \), \( y = 5 \) (the point \( (2,5) \)); when \( x=- 2 \), \( y = 5 \) (the point \( (-2,5) \)). Plot these points and draw a solid horizontal line through them.

Step3: Determine the region to shade

We need to find the region where \( y\geq5 \). This region is above the line \( y = 5 \). So we shade the area above the solid line \( y = 5 \).

(Note: Since this is a graphing problem, the final answer is the graph with a solid horizontal line at \( y = 5 \) and the region above the line shaded. But in text - based form, we can describe the steps to graph it as above.)

Answer:

1. Draw a solid horizontal line \( y = 5 \) (plot points like \((0,5)\), \((2,5)\), \((-2,5)\) etc. on this line).
2. Shade the region above the line \( y = 5 \).