Final answer:
The graphs of y = px and y = rx are perpendicular if the slopes p and r have a product of -1. Since p = | r |, the only solutions are p = 1 and r = -1, or p = -1 and r = 1, corresponding to opposite signs of slope due to the perpendicular lines.
Step-by-step explanation:
To find the values of p and r for the graphs of y = px and y = rx that are perpendicular to each other, we need to understand the concept of slopes of lines. Based on the equation y = mx + b, where m represents the slope, we know that for two lines to be perpendicular, the product of their slopes must be -1. So if the first line's slope is p and the second line's slope is r, the relationship pr = -1 must hold.
Since we are given that p = | r |, it means that p and r have the same magnitude but opposite signs. Therefore, if we choose p to be positive, r will be negative, and vice versa. Now, solving for p and r, we find that p can be either 1 or -1, and r will have the opposite sign. This is because only the values of 1 and -1 will satisfy both the condition pr = -1 and the given p = | r |. This also aligns with the notion that a positive slope indicates a positive correlation, which means an increase in x will increase y, while a negative slope indicates a negative correlation. In conclusion, the values of p and r that will result in two perpendicular graphs are p = 1 and r = -1, or p = -1 and r = 1.