Final answer:
A proportional relationship between x and y is confirmed when the ratio y/x remains constant. Given the points (1, 5), (2, 10), (3, 15), and (4, 20), the constant ratio of 5 verifies that y is directly proportional to x with a proportionality constant k of 5.
Step-by-step explanation:
A proportional relationship between two variables, x and y, exists if the ratio of x to y is constant. This means that as x increases or decreases, y does so at a consistent rate, represented by the equation y = kx, where k is the constant of proportionality. If we consider a table of values containing the points (1, 5), (2, 10), (3, 15), and (4, 20), we can test for proportionality by checking if the ratio y/x remains consistent for each pair of x and y values.
Given the points: (1, 5), (2, 10), (3, 15), and (4, 20)
- For (1, 5), the ratio is 5/1 = 5.
- For (2, 10), the ratio is 10/2 = 5.
- For (3, 15), the ratio is 15/3 = 5.
- For (4, 20), the ratio is 20/4 = 5.
The ratio y/x is constant at 5 for each point, confirming that the relationship between x and y is indeed proportional and follows the form y = kx with k equal to 5.