Direct Variation

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other. It can be expressed as y = kx, where k is the constant of proportionality.

Front

What is the constant of proportionality in direct variation?

Back

The constant of proportionality (k) is the constant factor that relates the two variables in a direct variation. It is the ratio of y to x.

Front

If y varies directly with x, what does this imply?

Back

This implies that as x increases, y increases proportionally, and as x decreases, y decreases proportionally.

Front

What is the equation for a direct variation where k = 5?

Back

The equation is y = 5x.

Front

How can you determine if a relationship is a direct variation from a table of values?

Back

A relationship is a direct variation if the ratio of y to x is constant for all pairs of values.

Front

If a person with a mass of 90 kg contains 60 kg of water, what is the constant of proportionality?

Back

The constant of proportionality is k = 60/90 = 2/3.

Front

What is the equation for the relationship between mass (m) and water (w) if w varies directly with m?

Back

The equation is w = km, where k is the constant of proportionality.

Front

If y = 60x, what is the value of y when x = 2?

Back

y = 60(2) = 120.

Front

True or False: The phrase 'y varies directly with x' indicates a direct variation relationship.

Back

True.

Front

Is the relationship in the table (1, 2), (2, 4), (3, 6) a direct variation?

Back

Yes, because the ratio of y to x is constant (2).