Final answer:
The inequality 2x + 3y ≥ -6 represents a region in the coordinate plane, with the line y = (-2/3)x - 2 as the boundary. The complete shading will occur in Quadrant III since this is where both x and y are negative and satisfy the inequality.
Step-by-step explanation:
To determine which quadrant will be completely shaded in the graph of the inequality 2x + 3y ≥ -6, we must first find the boundary line, which is the line where 2x + 3y = -6. If we solve for y, we get y = (-2/3)x - 2. The slope of this line is negative; hence, it will slope downwards from left to right.
To check which side of the line the inequality represents, we can plug in a test point not on the line such as (0,0). Since 2(0) + 3(0) is not greater than -6, the origin does not satisfy the inequality, and therefore, the area opposite to the origin side of the boundary line will be shaded. This will include Quadrant III where both x and y have negative values, and parts of Quadrants II and IV.