Proportional vs NonProportional

Front

What is a proportional relationship?

Back

A proportional relationship is one in which two quantities maintain a constant ratio, meaning that as one quantity increases or decreases, the other does so in a consistent manner. The graph of a proportional relationship is a straight line that passes through the origin.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one in which the ratio between two quantities is not constant. This means that the relationship does not maintain a consistent rate of change, and the graph does not pass through the origin.

Front

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

Back

A graph represents a proportional relationship if it is a straight line that passes through the origin (0,0). If the line does not pass through the origin, it is non-proportional.

Front

What does it mean if a relationship is described as 'proportional'?

Back

If a relationship is described as 'proportional', it means that there is a constant ratio between the two quantities involved, and the relationship can be expressed in the form y = kx, where k is a constant.

Front

What is the significance of the origin in proportional relationships?

Back

The origin (0,0) is significant in proportional relationships because it indicates that when one quantity is zero, the other quantity is also zero. This reflects the idea that there is no output without an input in a proportional relationship.

Front

What is the equation of a proportional relationship?

Back

The equation of a proportional relationship can be expressed in the form y = kx, where k is the constant of proportionality.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant factor (k) that relates two proportional quantities. It represents the ratio of the two quantities.

Front

How can you identify a non-proportional relationship from an equation?

Back

A non-proportional relationship can be identified from an equation if it includes a constant term that is not zero (e.g., y = kx + b, where b ≠ 0). This indicates that the relationship does not pass through the origin.

Front

What does the equation c = 7g + 25 represent in the context of catering?

Back

The equation c = 7g + 25 represents the total cost (c) for catering, where g is the number of guests. The term 7g represents the cost per guest, and 25 represents a fixed fee, indicating that this relationship is non-proportional.

Front

What is the graphical representation of a proportional relationship?

Back

The graphical representation of a proportional relationship is a straight line that passes through the origin, indicating a constant ratio between the two variables.