Finding K (Constant of Proportionality)

Front

What is the constant of proportionality?

Back

The constant of proportionality is the ratio between two proportional quantities, often represented by 'k'. It shows how one quantity changes in relation to another.

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 k = y/x.

Front

What does it mean if a relationship is proportional?

Back

A relationship is proportional if the ratio between the two quantities remains constant. This means that as one quantity increases, the other increases at a consistent rate.

Front

What is the equation of a proportional relationship?

Back

The equation of a proportional relationship is in the form y = kx, where k is the constant of proportionality.

Front

If k = 5, what does this mean in a real-world context?

Back

If k = 5, it means that for every unit increase in x, y increases by 5 units. For example, if x represents hours worked, y could represent money earned.

Front

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

Back

A table represents a proportional relationship if the ratios of corresponding values (y/x) are the same for all pairs.

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 $500 is earned for every 8 hours worked, what is the constant of proportionality?

Back

The constant of proportionality (k) is $500/8 hours = $62.50 per hour.

Front

What does the slope of a line in a proportional graph represent?

Back

The slope of a line in a proportional graph represents the constant of proportionality (k). It indicates how much y changes for a unit change in x.

Front

What is the significance of the origin (0,0) in a proportional relationship graph?

Back

The origin (0,0) signifies that when x is 0, y is also 0, indicating that there is no output without input in a proportional relationship.