Equations and Proportionality

Front

What is an equation with a constant of proportionality?

Back

An equation that can be expressed in the form y = kx, where k is the constant of proportionality.

Front

What does the constant of proportionality represent in an equation?

Back

It represents the ratio between two variables that are directly proportional to each other.

Front

How can you identify an equation with a constant of proportionality?

Back

Look for equations that can be rearranged into the form y = kx or x = ky.

Front

What is the unit rate in the context of proportional relationships?

Back

The unit rate is the constant of proportionality expressed as a ratio of two quantities, typically per one unit of the independent variable.

Front

Give an example of an equation with a constant of proportionality.

Back

y = 3x is an example, where the constant of proportionality is 3.

Front

What is the relationship between x and y in the equation y = 5/2x?

Back

y is directly proportional to x, with a constant of proportionality of 5/2.

Front

If y = kx, what happens to y if x is doubled?

Back

y will also double, since they are directly proportional.

Front

What is the formula to find the constant of proportionality from a proportional relationship?

Back

k = y/x, where k is the constant of proportionality.

Front

In the equation x = 2y, what is the constant of proportionality?

Back

The constant of proportionality is 1/2, since y = 1/2x.

Front

What does it mean if two quantities are directly proportional?

Back

It means that as one quantity increases, the other quantity increases at a constant rate.