Direct Variation Flashcard

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 a non-zero constant.

Front

How do you find the constant of variation in direct variation?

Back

To find the constant of variation (k), divide y by x (k = y/x) when given a pair of values for x and y.

Front

If y varies directly with x and y = 84 when x = 16, what is the constant of variation?

Back

k = y/x = 84/16 = 5.25.

Front

What is the equation representing the direct variation if y = 84 when x = 16?

Back

The equation is y = 5.25x.

Front

What does it mean if y varies inversely with x?

Back

If y varies inversely with x, it means that as x increases, y decreases, and vice versa. This can be expressed as y = k/x, where k is a constant.

Front

How do you find the constant of variation in inverse variation?

Back

To find the constant of variation (k) in inverse variation, multiply y by x (k = xy) when given a pair of values for x and y.

Front

If y = 150 when x = 2, what is the constant of variation for the inverse relationship?

Back

k = xy = 150 * 2 = 300.

Front

If y varies inversely with x and k = 300, what is y when x = 25?

Back

y = k/x = 300/25 = 12.

Front

If y varies directly with x, and y = 12 when x = 3, what is the value of y when x = 6?

Back

Since y varies directly, k = y/x = 12/3 = 4. Therefore, y = kx = 4 * 6 = 24.

Front

What is the formula to convert direct variation into an equation?

Back

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