Question

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: Analyze the inequality

The inequality is \( y \geq 7 \). This represents all the points where the \( y \)-coordinate is greater than or equal to 7.

Step2: Determine the boundary line

Since the inequality is \( \geq \), the boundary line \( y = 7 \) is a solid line (because the inequality includes equality). To plot the boundary line, we can find points where \( y = 7 \). For example, when \( x = 0 \), \( y = 7 \) (point \( (0, 7) \)); when \( x = 2 \), \( y = 7 \) (point \( (2, 7) \)); when \( x = -3 \), \( y = 7 \) (point \( (-3, 7) \)), etc.

Step3: Determine the region to shade

We need to shade the region where \( y \geq 7 \). This is the region above the line \( y = 7 \) (including the line itself because of the \( \geq \) sign).

Answer:

To graph \( y \geq 7 \):

1. Draw a solid horizontal line at \( y = 7 \) (plot points like \( (0, 7) \), \( (2, 7) \), \( (-3, 7) \) on this line).
2. Shade the region above the line \( y = 7 \) (all points with \( y \)-coordinate 7 or greater).