Flashcard - Proportional vs Non-Proportional

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio. This means that as one quantity increases or decreases, the other does so in a consistent manner, represented by the equation y = kx, where k is a constant.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities is not constant. This can be represented by equations that include a constant term or do not pass through the origin.

Front

How can you identify a proportional relationship from a graph?

Back

A proportional relationship on a graph is represented by a straight line that passes through the origin (0,0).

Front

How can you identify a non-proportional relationship from a graph?

Back

A non-proportional relationship on a graph is represented by a straight line that does not pass through the origin or a curve.

Front

What does the equation y = kx represent?

Back

The equation y = kx represents a proportional relationship, where k is the constant of proportionality.

Front

What does the equation y = mx + b represent?

Back

The equation y = mx + b represents a linear relationship, where m is the slope and b is the y-intercept. If b is not zero, it is non-proportional.

Front

If a table shows the values (1,2), (2,4), (3,6), what type of relationship is this?

Back

This table shows a proportional relationship because the ratio of y to x is constant (y/x = 2).

Front

If a table shows the values (1,3), (2,5), (3,7), what type of relationship is this?

Back

This table shows a non-proportional relationship because the ratio of y to x is not constant.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant factor (k) that relates two proportional quantities in the equation y = kx.

Front

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

Back

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