Finding the Constant of Proportionality

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant value (k) that relates two proportional quantities, defined as k = y/x.

Front

How do you identify the constant of proportionality from a table?

Back

To identify the constant of proportionality from a table, divide the value of y by the value of x for any pair of corresponding values.

Front

What does it mean if a relationship is proportional?

Back

A relationship is proportional if the ratio of the two quantities remains constant.

Front

If k = 5, what does this indicate about the relationship between x and y?

Back

It indicates that for every unit increase in x, y increases by 5 units.

Front

What is the formula to find the constant of proportionality?

Back

The formula to find the constant of proportionality is k = y/x.

Front

If a table shows (2, 6), (4, 12), and (6, 18), is this a proportional relationship?

Back

Yes, the constant of proportionality is 3 (k = 6/2 = 12/4 = 18/6).

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together, expressed as a quantity per one unit of another quantity.

Front

If the unit rate is 0.5 swings per day, what does this mean?

Back

It means that for every day, there are 0.5 swings, or one swing every two days.

Front

What is the significance of the constant of proportionality in real-life situations?

Back

It helps to understand relationships between quantities, such as speed, density, and price per item.

Front

How can you tell if a relationship is not proportional?

Back

If the ratio of y to x changes for different pairs of values, the relationship is not proportional.