Proportional Relationships: Tables, Equations, and Graphs

Front

What is the constant of proportionality?

Back

The constant of proportionality is the ratio between two proportional quantities, often represented as k. For example, if k = 15 gallons of water per minute, it means for every minute, 15 gallons of water is used.

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. For example, if you buy 3 watermelons for $9, the unit rate is $3 per watermelon.

Front

How can you tell if a table of values is proportional?

Back

Front

What makes a graph proportional?

Back

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

Front

What is the equation of a proportional relationship?

Back

The equation of a proportional relationship can be expressed in the form y = kx, where k is the constant of proportionality.

Front

If k = 20 gallons of water per minute, what is the relationship between y and x?

Back

The relationship can be expressed as y = 20x, where y is the total gallons of water used and x is the time in minutes.

Front

What does it mean if a graph does not go through the origin?

Back

If a graph does not go through the origin, it indicates that the relationship is not proportional.

Front

How do you find the constant of proportionality from a table?

Back

To find the constant of proportionality from a table, divide the y-value by the corresponding x-value for any point in the table. If the result is the same for all points, that value is k.

Front

What is the unit rate for 5 apples costing $10?

Back

The unit rate is $2 per apple, calculated by dividing the total cost by the number of apples.

Front

What is the significance of the origin in proportional relationships?

Back

The origin (0,0) is significant in proportional relationships because it indicates that when there is no input (x=0), the output (y) is also zero.