Proportional Relationships in Various Representations

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other quantity is constant.

Front

What does it mean for a graph to represent a proportional relationship?

Back

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

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant ratio between two proportional quantities, often represented as 'k' in the equation y = kx.

Front

How can you determine if two rates are equal?

Back

Two rates are equal if the ratio of the two quantities is the same, meaning they have the same constant of proportionality.

Front

What is the formula to find the constant of proportionality from a table of values?

Back

The constant of proportionality can be found by dividing the output value by the input value (k = y/x).

Front

If a graph does not pass through the origin, what can be concluded about its proportionality?

Back

If a graph does not pass through the origin, it does not represent a proportional relationship.

Front

In a proportional relationship, what happens to one quantity if the other quantity is doubled?

Back

If one quantity is doubled in a proportional relationship, the other quantity also doubles.

Front

What is the relationship between the slope of a line and proportional relationships?

Back

In a proportional relationship, the slope of the line represents the constant of proportionality.

Front

How do you find the number of cups of blue paint needed if the ratio of blue to white paint is 2 to 5?

Back

To find the number of cups of blue paint needed, set up a proportion: (blue/white) = (2/5). If there are 45 cups of white paint, then blue = (2/5) * 45 = 18 cups.

Front

What does it mean for speed to be directly proportional to energy consumed?

Back

It means that as speed increases, the energy consumed increases at a constant rate.