In the diagram overline (BD) is a diameter of circle A. If the slope of overleftrightarrow (BE) is (3)/(2) what is the slope of overleftrightarrow (BD) A. (3)/(2) B. -(3)/(2) C. (2)/(3) D. -(2)/(3)

To find the slope of line , we need to use the fact that is the diameter of the circle and is also a diameter as given in the question. Since and are both diameters of the same circle and share the endpoint , they must coincide and thus are the same line.Now, we know that intersects the diameter (which is the same as ) at point . Since has a slope of , the line perpendicular to it (which would be the diameter ) will have a slope that is the negative reciprocal of .The negative reciprocal of is calculated by flipping the fraction and changing the sign, which gives us .Therefore, the slope of is .The final answer is:D.