Inverse Variation

Front

What is inverse variation?

Back

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

Front

Which equation represents an inverse variation?

Back

y = 40/x

Front

If y varies inversely as x, what is the relationship between y and x?

Back

The relationship is y = k/x, where k is a constant.

Front

Given the points (32, 15) and (12, y), how do you find the constant k?

Back

Use the formula k = xy. For (32, 15), k = 32 * 15 = 480.

Front

If k = 480 and x = 12, what is y?

Back

y = k/x = 480/12 = 40.

Front

If y = -3 when x = -6, what is the constant k?

Back

k = xy = -3 * -6 = 18.

Front

If y varies inversely as x and k = 18, what is y when x = 14?

Back

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

Front

What does the graph of an inverse variation look like?

Back

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

Front

Which of the following represents direct variation?

Back

y = kx.

Front

What is the difference between direct and inverse variation?

Back

In direct variation, y = kx (as one variable increases, the other increases). In inverse variation, y = k/x (as one variable increases, the other decreases).