Proportional Relationships in Tables, Graphs, and Equations

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 that for every minute, 15 gallons of water are used.

Front

How can you determine if a set of data is proportional?

Back

A set of data is proportional if the unit rate (the ratio of the quantities) is constant across all data points. If the unit rate varies, the relationship is not proportional.

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It expresses how much of one quantity corresponds to one unit of another quantity, such as 2 cm of rainfall per hour.

Front

What does a proportional relationship look like on a graph?

Back

A proportional relationship on a graph is represented by a straight line that passes through the origin (0,0). The slope of the line represents the constant of proportionality.

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

How do you identify proportional relationships in tables?

Back

To identify proportional relationships in tables, check if the ratios of corresponding values are constant. If they are, the relationship is proportional.

Front

What is the significance of the slope in a proportional relationship?

Back

The slope of a line in a proportional relationship represents the constant of proportionality, indicating how much one quantity changes in relation to another.

Front

What are some examples of proportional relationships in real life?

Back

Examples of proportional relationships include speed (distance per time), density (mass per volume), and price per item.

Front

How can you convert a proportional relationship into an equation?

Back

To convert a proportional relationship into an equation, identify the constant of proportionality (k) and use the formula y = kx, where x is the independent variable.

Front

What does it mean if a table of values is not proportional?

Back

If a table of values is not proportional, it means that the ratios of the corresponding values are not constant, indicating that the relationship between the quantities is not linear.