Direct and Inverse 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 Inverse Variation?

Back

Inverse variation is a relationship between two variables where the product of the two variables is a constant. It can be expressed as xy = k, where k is the constant.

Front

Identify the equation of direct variation: y = -2x, y = x + 5, y = rac{1}{x}, y = 3x + 1.

Back

y = -2x

Front

Identify the equation of inverse variation: y = 3x, y = rac{12}{x}, y = 4x + 1, y = -x.

Back

y = \frac{12}{x}

Front

What is the constant of variation in the equation y = 5x?

Back

The constant of variation is 5.

Front

Determine if the following table represents direct variation: (1, 2), (2, 4), (3, 6). What is the constant?

Back

Yes; the constant is 2.

Front

Determine if the following table represents direct variation: (1, 3), (2, 5), (3, 7).

Back

No

Front

Write the equation for the direct variation where the constant is 1/4.

Back

y = \frac{1}{4}x

Front

What is the relationship between x and y in direct variation?

Back

In direct variation, as x increases, y increases proportionally.

Front

What is the relationship between x and y in inverse variation?

Back

In inverse variation, as x increases, y decreases, and vice versa.