Proportional vs. Non-Proportional

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio or unit rate. This means that as one quantity increases, the other quantity 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. This can occur when there is an additional fixed cost or when the relationship does not pass through the origin.

Front

How can you determine if a relationship is proportional using a table of values?

Back

A relationship is proportional if the ratios of corresponding values are constant across the table. If the unit rate changes, the relationship is non-proportional.

Front

What does it mean for a graph to pass through the origin?

Back

A graph passes through the origin if the point (0,0) is on the graph. This indicates that when one quantity is zero, the other quantity is also zero, which is a characteristic of proportional relationships.

Front

What is a unit rate?

Back

A unit rate is a ratio that compares a quantity to one unit of another quantity. It is often expressed as 'x per 1 unit'.

Front

If a pie costs $4.50 and there is a $5 delivery charge for orders less than a dozen, is the total cost proportional to the number of pies ordered?

Back

No, the total cost is non-proportional because of the additional fixed delivery charge.

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept is the point where the graph crosses the y-axis. In proportional relationships, the y-intercept is always zero.

Front

How can you identify a proportional graph?

Back

A proportional graph is a straight line that passes through the origin (0,0). The slope of the line represents the constant unit rate.

Front

What does it mean if a table of values does not pass through the origin?

Back

If a table of values does not pass through the origin, it indicates that the relationship is non-proportional, often due to a fixed cost or starting value.

Front

What is the unit rate if a car travels 18 miles in 2 hours?

Back

The unit rate is 9 miles per hour.