Tables: Proportional or Non-proportional

Front

What is a proportional relationship?

Back

A proportional relationship is one in which two quantities maintain a constant ratio or rate. If one quantity increases, the other increases at a consistent rate.

Front

What is the constant of proportionality?

Back

The constant of proportionality (k) is the constant value that relates two proportional quantities. It can be found by dividing one quantity by the other.

Front

How can you determine if a table represents a proportional relationship?

Back

To determine if a table represents a proportional relationship, check if the ratios of corresponding values are constant.

Front

What does it mean if a relationship is non-proportional?

Back

A non-proportional relationship means that the ratio between two quantities is not constant; as one quantity changes, the other does not change at a consistent rate.

Front

If y = kx, what does k represent?

Back

In the equation y = kx, k represents the constant of proportionality, indicating how much y changes for each unit change in x.

Front

Example of a proportional relationship: If x = 2 and y = 6, what is k?

Back

k = y/x = 6/2 = 3.

Front

Example of a non-proportional relationship: If x = 1, y = 2; if x = 2, y = 5, is this proportional?

Back

No, because the ratios (2/1 and 5/2) are not constant.

Front

What is the graphical representation of a proportional relationship?

Back

The graphical representation of a proportional relationship is a straight line that passes through the origin (0,0).

Front

What is the formula to find the constant of proportionality from a table?

Back

To find the constant of proportionality, divide the value of y by the value of x (k = y/x).

Front

If a table shows (1, 4), (2, 8), (3, 12), is it proportional?

Back

Yes, it is proportional because the ratio y/x = 4/1 = 8/2 = 12/3 = 4.