Identify Proportional and Non-Proportional Relationships

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 can you identify a proportional relationship from a graph?

Back

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

Front

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

Back

A graph represents a non-proportional relationship if it is a straight line that does not pass through the origin or if it is not a straight line.

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 that is non-proportional if b is not equal to zero.

Front

If y = 3x, is this relationship proportional or non-proportional?

Back

Proportional, because it can be expressed in the form y = kx.

Front

If y = 2x + 5, is this relationship proportional or non-proportional?

Back

Non-proportional, because it includes a constant term (5) that shifts the line.

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

Can a table of values show a proportional relationship?

Back

Yes, a table of values shows a proportional relationship if the ratios of corresponding values are constant.