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Which representation shows a proportional relationship between x and y?

Option 1: 20
Option 2: 15
Option 3: 10
Option 4: 12.

1 Answer

7 votes

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.

User Pd Shah
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