Constant of Proportionality

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant value (k) that relates two proportional quantities, defined as k = y/x.

Front

How do you identify the constant of proportionality from a table?

Back

To identify the constant of proportionality from a table, divide the value of y by the corresponding value of x for any pair of values. If the result is the same for all pairs, that value is k.

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 = 3, what does this mean in a real-world context?

Back

If k = 3, it means that for every 1 unit of x, y increases by 3 units.

Front

Is the relationship between x and y proportional if k = 0?

Back

No, if k = 0, the relationship is not proportional; it indicates that y is always 0 regardless of x.

Front

What does it mean if a graph passes through the origin?

Back

If a graph passes through the origin, it indicates a proportional relationship between the variables.

Front

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

Back

A table represents a proportional relationship if the ratio of y to x is constant for all pairs of values.

Front

What is the constant of proportionality if y = 12 when x = 4?

Back

The constant of proportionality k = y/x = 12/4 = 3.

Front

If a boat travels 60 miles in 2 hours, what is the constant of proportionality?

Back

The constant of proportionality k = 60 miles / 2 hours = 30 miles per hour.

Front

What is the significance of the constant of proportionality in a graph?

Back

The constant of proportionality indicates the steepness of the line in a graph representing a proportional relationship.