Multiple Representations

Front

What is a proportional relationship?

Back

A proportional relationship is one in which two quantities maintain a constant ratio. For example, if y = kx, where k is a constant, then y is proportional to x.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities is not constant. For example, y = mx + b (where b ≠ 0) represents a non-proportional relationship.

Front

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

Back

Check if the ratios of corresponding values are constant. If they are not, the relationship is non-proportional.

Front

What is the rate of change?

Back

The rate of change is a measure of how much a quantity changes in relation to another quantity. It is often represented as the slope in a linear equation.

Front

What does a constant slope indicate?

Back

A constant slope indicates a linear relationship, meaning the rate of change is the same throughout.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant factor (k) in the equation y = kx, representing the ratio of y to x.

Front

How can you find the constant of proportionality from a word problem?

Back

Identify the quantities involved, determine their ratio, and simplify to find the constant.

Front

What does it mean if a relationship is not proportional?

Back

It means that the relationship does not maintain a constant ratio, often indicated by a non-zero y-intercept in a linear equation.

Front

What is an example of a proportional relationship in real life?

Back

An example is the relationship between distance and time when traveling at a constant speed.

Front

What is an example of a non-proportional relationship?

Back

An example is the relationship between the number of items purchased and the total cost when there is a fixed delivery fee.