Inverse Variation

Front

What is inverse variation?

Back

Inverse variation is a relationship between two variables where the product of the variables is constant. If y varies inversely as x, then y = k/x, where k is a non-zero constant.

Front

If y = -3 when x = -6, what is the constant k in the inverse variation equation?

Back

k = y * x = -3 * -6 = 18.

Front

Find y when x = 14 if y varies inversely as x and k = 18.

Back

y = k/x = 18/14 = 9/7.

Front

What does the graph of inverse variation look like?

Back

The graph of inverse variation is a hyperbola that approaches the axes but never touches them.

Front

Does the equation y = 10/x represent inverse variation?

Back

Yes, it represents inverse variation because it can be expressed in the form y = k/x.

Front

What is the general form of a direct variation equation?

Back

The general form of a direct variation equation is y = kx, where k is a non-zero constant.

Front

Identify the type of variation: y = k/x.

Back

Inverse variation.

Front

Identify the type of variation: y = mx + b.

Back

This represents a linear equation, not a variation.

Front

What is the constant k in the equation y = 54/x?

Back

k = 54.

Front

If y varies inversely as x and y = 6 when x = 3, what is y when x = 9?

Back

y = k/x; k = 6 * 3 = 18; y = 18/9 = 2.