Proportional vs. Non-Proportional

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio, meaning as one quantity increases, the other increases at a consistent rate.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities is not constant, meaning the relationship does not maintain a consistent rate of change.

Front

How can you identify a proportional relationship from a graph?

Back

A graph represents a proportional relationship if it is a straight line that passes through the origin (0,0).

Front

How can you identify a non-proportional relationship from a graph?

Back

A graph represents a non-proportional relationship if it is a straight line that does not pass through the origin or if it is not a straight line.

Front

What does the equation y = mx + b represent?

Back

This equation represents a linear function where 'm' is the slope and 'b' is the y-intercept. If b is not zero, the relationship is non-proportional.

Front

What is the slope in a proportional relationship?

Back

In a proportional relationship, the slope (m) is constant and represents the ratio of the change in y to the change in x.

Front

Give an example of a proportional relationship in real life.

Back

An example is a taxi fare that charges a fixed rate per mile without any additional fees.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept indicates the value of y when x is zero. In a proportional relationship, the y-intercept is always zero.

Front

How do you determine if a table shows a proportional relationship?

Back

A table shows a proportional relationship if the ratios of corresponding values (y/x) are constant.

Front

What is an example of a non-proportional function?

Back

An example is y = 2x + 3, where the y-intercept is not zero, indicating a non-proportional relationship.