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 variation.

Front

What is the constant of proportionality in direct variation?

Back

The constant of proportionality, denoted as k, is the constant factor that relates the two variables in a direct variation. It can be found using the formula k = \frac{y}{x}.

Front

If y varies directly with x and y = 10 when x = 5, what is the equation of variation?

Back

The equation is y = 2x.

Front

How do you determine if a relationship is a direct variation?

Back

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

Front

What is the formula to find y when x is known in direct variation?

Back

The formula is y = kx, where k is the constant of variation.

Front

If y = 3 when x = 9, what is y when x = 12?

Back

y = 4 when x = 12.

Front

What does it mean if k is positive in direct variation?

Back

If k is positive, it means that as x increases, y also increases.

Front

What does it mean if k is negative in direct variation?

Back

If k is negative, it means that as x increases, y decreases.

Front

If the total cost of items varies directly with the number of items, what is the equation?

Back

The equation is C = kN, where C is the total cost, N is the number of items, and k is the cost per item.

Front

If y = 8 when x = 4, find the value of k.

Back

k = 2.