Rates and Proportionality

Front

What does 'constant of proportionality' represent in a proportional relationship?

Back

The constant of proportionality is the ratio between two proportional quantities, often represented by the letter 'k'.

Front

What is the formula to find the constant of proportionality in a proportion?

Back

k = y/x, where y is the dependent variable and x is the independent variable.

Front

If a table shows the values (1, 2), (2, 4), (3, 6), what is the constant of proportionality?

Back

k = 2, since for every increase in x by 1, y increases by 2.

Front

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

Back

A graph represents a proportional relationship if it passes through the origin (0,0) and is a straight line.

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where their ratio remains constant.

Front

If k = 3, what does this imply about the relationship between x and y?

Back

It implies that for every unit increase in x, y increases by 3 units.

Front

What is the significance of the point (0,0) in a proportional relationship?

Back

The point (0,0) indicates that when there is no input (x=0), the output (y) is also zero, confirming the relationship is proportional.

Front

If a recipe requires 2 cups of flour for every 3 cups of sugar, what is the constant of proportionality?

Back

k = 2/3, meaning for every 2 cups of flour, there are 3 cups of sugar.

Front

What does it mean if a relationship is not proportional?

Back

It means that the ratio between the two quantities is not constant; as one quantity changes, the other does not change in a consistent manner.

Front

How do you solve for k in the equation 4k = 20?

Back

Divide both sides by 4: k = 20/4, so k = 5.