Proportional v. Non Proportional

Front

What is a proportional relationship?

Back

A proportional relationship is one in which two quantities maintain a constant ratio. If one quantity increases, the other increases at the same rate.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities is not constant. Changes in one quantity do not result in consistent changes in the other.

Front

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

Back

A proportional relationship can be identified if the ratio of y to x is constant for all pairs of values in the table.

Front

If y varies directly as x, what does this mean?

Back

It means that y is equal to a constant multiplied by x (y = kx), where k is the constant of proportionality.

Front

Given x = 27 when y = 6, find the constant of proportionality (k).

Back

k = y/x = 6/27 = 2/9.

Front

If y = 2, what is x when y varies directly as x and k = 2/9?

Back

x = y/k = 2/(2/9) = 9.

Front

What does a straight line through the origin on a graph indicate?

Back

It indicates a proportional relationship between the two variables.

Front

What does a straight line not passing through the origin indicate?

Back

It indicates a non-proportional relationship between the two variables.

Front

How can you tell if a graph is non-proportional?

Back

A graph is non-proportional if it does not pass through the origin or if the slope is not constant.

Front

What is the slope in a proportional relationship?

Back

The slope is the constant ratio of y to x, which remains the same for all points on the line.