Direct & 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 a non-zero constant.

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 y = k/x, where k is a non-zero constant.

Front

If y varies directly with x and y = 10 when x = 2, what is the equation?

Back

y = 5x.

Front

If y varies inversely with x and y = 3 when x = 6, what is the equation?

Back

y = 18/x.

Front

What does the constant k represent in direct variation?

Back

In direct variation, k represents the constant of proportionality, indicating how much y changes for a unit change in x.

Front

What does the constant k represent in inverse variation?

Back

In inverse variation, k represents the constant product of the two variables, indicating that as one variable increases, the other decreases.

Front

If y varies directly with the square of x, what is the equation?

Back

y = kx², where k is a constant.

Front

How do you find k in a direct variation problem?

Back

To find k, divide y by x (k = y/x) using known values of y and x.

Front

How do you find k in an inverse variation problem?

Back

To find k, multiply y by x (k = y * x) using known values of y and x.

Front

If y = 2/x, what happens to y as x increases?

Back

As x increases, y decreases, demonstrating the inverse relationship.