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. This relationship can be represented by a straight line that passes through the origin (0,0).

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 as one quantity changes, the other does not change in a consistent manner, and the graph of this relationship 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 graph does not pass through the origin?

Back

If a graph does not pass through the origin, it indicates that the relationship between the two variables is non-proportional, meaning there is a constant added value or intercept.

Front

What is the significance of the slope in a proportional relationship?

Back

In a proportional relationship, the slope represents the constant ratio between the two quantities. The slope is the same at all points on the line.

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 equation of a non-proportional relationship?

Back

The equation of a non-proportional relationship can be expressed in the form y = mx + b, where b is not equal to zero, indicating a y-intercept.

Front

How can you identify a non-proportional equation?

Back

A non-proportional equation can be identified if it includes a constant term (y-intercept) that is not zero, such as in the equation y = mx + b where b ≠ 0.

Front

What is the relationship between proportionality and direct variation?

Back

Proportionality is a specific case of direct variation where two quantities vary directly with each other, maintaining a constant ratio.

Front

Can a proportional relationship be represented in a table?

Back

Yes, a proportional relationship can be represented in a table where the ratio of corresponding values remains constant.