Proportional vs. Nonproportional

Front

What is a proportional relationship?

Back

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

Front

What is a nonproportional relationship?

Back

A nonproportional relationship is one where the ratio between two quantities is not constant. For example, y = mx + b (where b ≠ 0) represents a nonproportional 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 nonproportional relationship from a graph?

Back

A graph represents a nonproportional relationship if it is a straight line that does not pass through the origin.

Front

What is the constant of proportionality?

Back

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

Front

If y = 3x, what is the constant of proportionality?

Back

The constant of proportionality is 3.

Front

If y = 2x + 5, is this a proportional relationship?

Back

No, this is a nonproportional relationship because it has a y-intercept of 5.

Front

What does it mean if a table shows a constant ratio?

Back

If a table shows a constant ratio, it indicates that the relationship between the two quantities is proportional.

Front

What is an example of a nonproportional table?

Back

A table showing values like (1, 2), (2, 5), (3, 8) is nonproportional because the ratios between x and y are not constant.

Front

What is the slope of a proportional relationship graph?

Back

The slope of a proportional relationship graph is equal to the constant of proportionality.