Constant of Proportionality (COP)

Front

What is the constant of proportionality (COP)?

Back

The constant of proportionality (COP) is a constant value that relates two proportional quantities. It is the ratio of one quantity to another when the two quantities are directly proportional.

Front

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

Back

To find the constant of proportionality from a graph, identify two points on the line, (x1, y1) and (x2, y2), and use the formula COP = y/x.

Front

What does a constant of proportionality of 3 mean in a table of values?

Back

It means that for every 1 unit increase in the independent variable, the dependent variable increases by 3 units.

Front

Is the relationship between the quantities in the table proportional if the COP is constant?

Back

Yes, if the constant of proportionality is the same for all pairs of values in the table, the relationship is proportional.

Front

What does it mean if a graph does not represent a proportional relationship?

Back

It means that the ratio of the dependent variable to the independent variable is not constant across the graph.

Front

How can you tell if a graph represents a proportional relationship?

Back

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

Front

If the COP is 45, how far does a boat travel in 1 hour?

Back

The boat travels 45 miles in 1 hour.

Front

What is the significance of the constant of proportionality in real-life situations?

Back

The constant of proportionality helps to understand relationships between quantities, such as speed, density, and cost per item.

Front

What is an example of a proportional relationship in everyday life?

Back

An example is the relationship between distance and time when traveling at a constant speed.

Front

If a table shows values (1, 3), (2, 6), (3, 9), what is the COP?

Back

The constant of proportionality is 3, as each y-value is 3 times the corresponding x-value.