Question

Does this table show a proportional relationship? I think no but I feel a bit confused

Answer 1

To determine if a table shows a proportional relationship, we check if the ratio of y to x is constant for all data pairs or if the correlation coefficient indicates a significant linear relationship. Without a consistent ratio or a correlation coefficient significantly different from zero, the relationship is not proportional.

Step-by-step explanation:

When assessing if a table shows a proportional relationship, we look for a consistent ratio between the two variables included, typically denoted as x and y. If when we calculate y/x for each pair of values the ratio is constant, then the relationship is proportional. This is equivalent to saying that the data points would fall on a straight line when plotted on a graph with a constant slope.

Professionals often analyze the correlation coefficient to determine the strength and direction of a linear relationship between two numeric variables. A correlation coefficient significantly different from zero suggests a strong linear relationship. However, if there is insufficient evidence to conclude there is a significant linear relationship because the correlation coefficient is not significantly different from zero, then the variables do not have a significant linear or proportional relationship.

To definitively answer whether the table shows a proportional relationship, we need to either calculate the ratio of y to x for each pair of data or determine the correlation coefficient. If the ratio is constant, or if the correlation coefficient is significantly different from zero, then the conclusion is that there is a proportional or significant linear relationship between x and y.

Answer 2

Answer:

NO

Step-by-step explanation:

For the table to show a proportional relationship, there must be a constant of proportionality that applies to every row in the table

`\begin{gathered} \text{If y }\propto\text{ x} \\ \text{Introducing a constant of proportionality, k} \\ y\text{ = kx} \\ k\text{ = }(y)/(x) \end{gathered}`

For x = 10, y = 60

k = y/x

k = 60/10

k = 6

For x = 2, y = 12

k = y/x

k = 12/2

k = 6

For x = 5, y = 35

k = y/x

k = 35/5

k = 7

Since k is not the same for all the rows in the table, the table does not show a proportional relationship