Proportional vs. Nonproportional

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other is constant. This means that as one quantity increases or decreases, the other quantity does so in a consistent manner.

Front

What does it mean if a graph passes through the origin?

Back

If a graph passes through the origin (0,0), it indicates that when one quantity is zero, the other quantity is also zero, which is a characteristic of proportional relationships.

Front

True or False: A proportional graph must pass through the origin.

Back

True

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is a relationship where the ratio between two quantities is not constant. This means that the quantities do not change in a consistent manner.

Front

How can you identify a proportional relationship from a table of values?

Back

A proportional relationship can be identified if the ratios of corresponding values are constant across the table.

Front

What is the slope of a line in a graph?

Back

The slope of a line is a measure of its steepness, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Front

If a graph intersects the y-axis at a point other than (0,0), what does that indicate?

Back

It indicates that the relationship is non-proportional, as it does not pass through the origin.

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 does the constant of proportionality represent?

Back

The constant of proportionality (k) represents the ratio between the two quantities in a proportional relationship.

Front

How can you tell if a graph is proportional by looking at its slope?

Back

If the slope is constant and the line passes through the origin, the graph represents a proportional relationship.