Final answer:
The supplied details erroneously describe a linear equation rather than the quadratic equation needed to answer the original question. The actual task is to find the value of b for the horizontal line y = b that equally partitions the area under the parabola y = 9 - x² and above the x-axis.
Step-by-step explanation:
The question appears to be incorrectly presenting the equations involved in the problem. The reference information provided repeatedly indicates that the line equation is y = 9 + 3x, which is a linear equation with a y-intercept of 9 and a slope of 3. This does not align with the original question, which asks about a horizontal line y = b and the division of an area bounded by y = 9 - x², a parabolic function, and y = 0, which is the x-axis. To find the value of b that divides the region into two equal areas, we would need to determine the area under the parabola from y = 0 to the y = b line and use integration or geometric methods to find the b value that makes that area equal to half of the total area under the parabola from y = 0 to its vertex.