Question

Which of the following tables represents a linear relationship that is also proportional? x −1 0 1 y 0 2 4 x −3 0 3 y −2 −1 0 x −2 0 2 y 1 0 −1 x −1 0 1 y −5 −2 1

Answer 1

x: -1, 0, 1

y: 0, 2, 4

Explanation:

A linear relationship is proportional if the ratio between the values of y and x remains constant for all data points. Let's analyze each table to determine if they represent a linear relationship that is also proportional:

x: -1, 0, 1

y: 0, 2, 4

In this case, when x increases by 1, y increases by 2. The ratio between the values of y and x is always 2. Therefore, this table represents a linear relationship that is proportional.

x: -3, 0, 3

y: -2, -1, 0

In this case, when x increases by 3, y increases by 1. The ratio between the values of y and x is not constant. Therefore, this table does not represent a linear relationship that is proportional.

x: -2, 0, 2

y: 1, 0, -1

In this case, when x increases by 2, y decreases by 1. The ratio between the values of y and x is not constant. Therefore, this table does not represent a linear relationship that is proportional.

x: -1, 0, 1

y: -5, -2, 1

In this case, when x increases by 1, y increases by 3. The ratio between the values of y and x is not constant. Therefore, this table does not represent a linear relationship that is proportional.