4.3 Constant of Proportionality

Front

What is the constant of proportionality?

Back

The constant of proportionality is a constant ratio between two proportional quantities, often represented as k.

Front

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

Back

A table represents a proportional relationship if the ratio of the values in one column to the corresponding values in another column is constant.

Front

What is the formula for finding the constant of proportionality?

Back

The formula for finding the constant of proportionality is k = y/x, where y is the dependent variable and x is the independent variable.

Front

If a table shows values (2, 6), (4, 12), and (6, 18), what is the constant of proportionality?

Back

The constant of proportionality is k = 3, since 6/2 = 12/4 = 18/6 = 3.

Front

What does a constant of proportionality of 0.20 indicate in a real-world context?

Back

A constant of proportionality of 0.20 indicates that for every unit increase in the independent variable, the dependent variable increases by 0.20 units.

Front

If the constant of proportionality is $9 per hour, what does this mean in a practical scenario?

Back

It means that for every hour worked, the payment or cost is $9.

Front

Can the constant of proportionality be a fraction? Provide an example.

Back

Yes, the constant of proportionality can be a fraction. For example, if k = 1/2, it means for every 2 units of x, y increases by 1 unit.

Front

What is the significance of identifying the constant of proportionality in a problem?

Back

Identifying the constant of proportionality helps in understanding the relationship between variables and allows for predictions based on that relationship.

Front

How can you verify if two quantities are proportional using a graph?

Back

Two quantities are proportional if the graph of their relationship is a straight line that passes through the origin.

Front

What is the relationship between the constant of proportionality and slope in a linear graph?

Back

In a linear graph, the constant of proportionality is equal to the slope of the line.