Question

graph the inequality in the coordinate plane. y≥7

Explanation:

Step1: Identify the boundary line

The inequality is \( y \geq 7 \). First, consider the equation \( y = 7 \). This is a horizontal line (since it has the form \( y = k \), where \( k = 7 \)) that passes through all points with a \( y \)-coordinate of 7. Since the inequality is \( \geq \), the boundary line should be solid (to include the points on \( y = 7 \)).

Step2: Determine the region to shade

For the inequality \( y \geq 7 \), we need to shade the region where the \( y \)-coordinate of the points is greater than or equal to 7. This is the region above the line \( y = 7 \) (since as \( y \) increases, we move up the coordinate plane).

Step3: Graph the boundary line and shade the region

• Draw the solid horizontal line \( y = 7 \) (it will be a horizontal line crossing the \( y \)-axis at \( (0, 7) \) and parallel to the \( x \)-axis).
• Shade the area above this line (all the grid squares where the \( y \)-value is 7 or more).

Answer:

To graph \( y \geq 7 \):

1. Draw a solid horizontal line at \( y = 7 \) (since the inequality includes equality, \( \geq \)).
2. Shade the region above the line \( y = 7 \) (all points where \( y \)-coordinate \( \geq 7 \)).