A proportional relationship in math is a relationship between two quantities where their ratio remains constant. This means that when one quantity increases or decreases, the other quantity does the same in a consistent way. For example, if you have a proportional relationship between the number of hours worked and the amount of money earned, working twice as many hours will result in earning twice as much money.
To express a proportional relationship mathematically, you can use the equation y = kx, where k is a constant called the constant of proportionality. In this equation, y and x represent the two quantities being compared. The constant k tells you how much y changes in response to changes in x.
A real-world example of a proportional relationship is how miles per hour relates to time and distance. If you travel at a constant speed, the distance you travel is directly proportional to the time spent traveling. If you drive at a speed of 60 miles per hour for 2 hours, you will cover 120 miles. If you double the time to 4 hours, you double the distance to 240 miles, illustrating the constant ratio of distance to time.