Final answer:
The conjecture that cannot be made is that the diagonals of the parallelogram are perpendicular. Diagonals of parallelograms are not necessarily perpendicular even if their slopes are negative reciprocals; this is a property of rectangles that are squares.
Step-by-step explanation:
The question asks which conjecture cannot be made about the slopes of the diagonals in a parallelogram. The diagonals of a parallelogram have slopes of 5/3 and -3/5. Given that these slopes are negative reciprocals of each other, we can infer that the diagonals are perpendicular. However, this is not a true characteristic of diagonals in a parallelogram; rather, it is a characteristic of a rectangle, a specific type of parallelogram where the diagonals are congruent and bisect each other, but they are not necessarily perpendicular unless the rectangle is a square.
In terms of slope appearance, a positive slope indicates that the line is rising as it moves from left to right. A negative slope, on the other hand, implies that the line is descending as it moves from left to right. Finally, a zero slope means that the line is horizontal and does not rise or fall.
Therefore, the conjecture that cannot be made about the parallelogram is that its diagonals are perpendicular just because their slopes are negative reciprocals of one another. This is a property unique to rectangles that are squares.