Final answer:
A set of information shows a proportional relationship in mathematics if there is a consistent ratio between the values of the variables involved. This can be determined by graphing the data as a straight line passing through the origin or by calculating the ratio between corresponding values.
Step-by-step explanation:
In mathematics, a set of information shows a proportional relationship if there is a consistent ratio between the values of the variables involved. This means that as one variable increases or decreases, the other variable changes in a predictable way. One way to determine if a set of information shows a proportional relationship is by graphing the data and observing if it forms a straight line passing through the origin. If the graph shows a straight line, then the variables are directly proportional.
For example, if we have a set of data where the time spent running (x) and the distance covered (y) are recorded, and it is found that for every 5 minutes of running, the distance covered is 1 kilometer, then we can say that there is a proportional relationship between time and distance. This can be represented by the equation y = 1/5x.
Another way to determine if there is a proportional relationship is by calculating the ratio between corresponding values of the variables. If the ratio remains the same for all pairs of corresponding values, then the set of information shows a proportional relationship.