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).

Tags

CCSS.7.RP.A.2D

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.

Tags

CCSS.7.RP.A.2D

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.

Tags

CCSS.7.RP.A.2D

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.

Tags

CCSS.7.RP.A.2D

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.7.RP.A.2C

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.7.RP.A.2D

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.

Tags

CCSS.7.RP.A.2D

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.

Tags

CCSS.7.RP.A.2A