Proportional vs Non-Proportional 8.5H

Front

What is a proportional relationship?

Back

A proportional relationship is one in which two quantities increase or decrease at the same rate, meaning their ratio remains constant.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities is not constant, often represented by a linear equation with a non-zero y-intercept.

Front

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

Back

In a table of values, a proportional relationship will show that the ratio of y to x is constant for all pairs of values.

Front

What does the equation y = kx represent?

Back

The equation y = kx represents a proportional relationship where k is the constant of proportionality.

Front

What does the equation y = mx + b represent?

Back

The equation y = mx + b represents a linear relationship that is non-proportional if b (the y-intercept) is not zero.

Front

If a line passes through the origin, what type of relationship does it represent?

Back

If a line passes through the origin, it represents a proportional relationship.

Front

What is the significance of the y-intercept in determining proportionality?

Back

The y-intercept indicates whether a relationship is proportional; if it is zero, the relationship is proportional; if it is not zero, the relationship is non-proportional.

Front

Can a relationship be proportional if the slope is negative?

Back

Yes, a relationship can be proportional even if the slope is negative, as long as it passes through the origin.

Front

What is an example of a proportional relationship in real life?

Back

An example of a proportional relationship is the relationship between distance and time when traveling at a constant speed.

Front

What is an example of a non-proportional relationship?

Back

An example of a non-proportional relationship is the cost of a taxi ride, which includes a base fare plus a charge per mile.