Constant of Proportionality Skills

Front

What is the constant of proportionality?

Back

The constant of proportionality is a constant ratio or unit rate in a proportional relationship, often represented as 'k' in the equation y = kx.

Front

How do you find the unit rate?

Back

To find the unit rate, divide the total amount by the number of units. For example, if a box of cereal costs $3.59 for 30 oz, the unit rate is $3.59 ÷ 30 oz = $0.1197 per oz, rounded to 12 cents.

Front

What is the equation form of a proportional relationship?

Back

A proportional relationship can be written as y = kx, where 'y' is the dependent variable, 'k' is the constant of proportionality, and 'x' is the independent variable.

Front

If Justin ordered 5 ice cream bars for $12.25, how much was each ice cream bar?

Back

Each ice cream bar costs $12.25 ÷ 5 = $2.45.

Front

What does it mean if two quantities are proportional?

Back

Two quantities are proportional if they maintain a constant ratio or unit rate, meaning as one quantity increases, the other quantity increases at a consistent rate.

Front

How can you express a proportional relationship using a table?

Back

A proportional relationship can be expressed in a table by listing pairs of values that maintain the same ratio. For example, if k = 3, the pairs (1,3), (2,6), (3,9) show a proportional relationship.

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It is often expressed as a quantity per one unit of another quantity.

Front

If the constant of proportionality is 3/10, what does this mean in a real-world context?

Back

If the constant of proportionality is 3/10, it means for every 10 units of one quantity, there are 3 units of another quantity, indicating a consistent ratio.

Front

How do you determine if a relationship is proportional from a graph?

Back

A relationship is proportional if the graph is a straight line that passes through the origin (0,0). This indicates a constant ratio between the two variables.

Front

What is the relationship between unit rate and constant of proportionality?

Back

The unit rate is the same as the constant of proportionality in a proportional relationship, as both represent the ratio of one quantity to another.