Question

Does the following table show a proportional relationship between the variables \[x\] and \[y\]? \[x\] \[\dfrac{1}4\] \[\dfrac{2}4\] \[\dfrac{3}4\] \[y\] \[3\] \[6\] \[9\]

Answer 1

Yes, the table shows a proportional relationship between the variables x and y because there is a constant of proportionality. Therefore, the correct answer is: A. Yes.

In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:

y = kx

Where:

• y represents the y-variable​.
• x represents the x-variable.
• k is the constant of proportionality.

Next, we would determine the constant of proportionality (k) by using various data points in the table as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 3/(1/4) = 6/(2/4) = 9/(3/4)

Constant of proportionality, k = (3 × 4) = (6 × 4)/4 = (9 × 4)/3

Constant of proportionality, k = 12 = 12 = 12.

In conclusion, this table shows a proportional relationship between the variables x and y because it has a constant of proportionality of 12.

Complete Question:

Does the following table show a proportional relationship between the variables x and y.

A. Yes.

B. No.