Proportional VS. Non Proportional

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities increase or decrease at the same rate, represented by the equation y = kx, where k is a 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 equations that include a constant term or do not pass through the origin.

Front

Example of a proportional relationship:

Back

If a car travels at a constant speed of 60 miles per hour, the distance traveled (d) is proportional to the time (t) with the equation d = 60t.

Front

Example of a non-proportional relationship:

Back

If a video game rental fee is $15 plus $3 per day, the total cost is non-proportional because it includes a fixed fee.

Front

What does the equation y = 75x represent?

Back

This equation represents a proportional relationship where y increases 75 times for every unit increase in x.

Front

Does the equation y = 3x + 5 show a proportional relationship?

Back

No, because it includes a constant term (5) that shifts the line up, meaning it does not pass through the origin.

Front

Identify a non-proportional situation:

Back

Total fees charged for carpet cleaning where the first room costs $40 and each additional room costs $25.

Front

Identify a proportional situation:

Back

Total earnings from babysitting at a rate of $8 per hour, where earnings increase directly with hours worked.

Front

What is the graph of a proportional relationship like?

Back

The graph is a straight line that passes through the origin (0,0).

Front

What is the graph of a non-proportional relationship like?

Back

The graph is a straight line that does not pass through the origin, indicating a fixed starting value.