Jan 7 Inverse Variation

Front

What is inverse variation?

Back

Inverse variation is a relationship between two variables, x and y, such that when one variable increases, the other decreases. Mathematically, it can be expressed as y = k/x, where k is a constant.

Front

If y varies inversely with x, what is the product of x and y?

Back

The product of x and y is a constant (k). This means that x * y = k.

Front

Given y = 150 when x = 2, find the constant k.

Back

k = x * y = 2 * 150 = 300.

Front

If y = 12 when x = 25, is this an inverse variation with the previous values?

Back

Yes, because k remains constant. k = 25 * 12 = 300.

Front

How do you find y when x is given in an inverse variation?

Back

Use the formula y = k/x, where k is the constant found from previous values.

Front

If y = 23 when x = 8, find y when x = 4.

Back

y = k/x; k = 23 * 8 = 184; y = 184/4 = 46.

Front

What does a table showing inverse variation look like?

Back

A table showing inverse variation will have pairs of (x, y) values where the product x * y is constant.

Front

If y = 15 when x = 32, find y when x = 12.

Back

k = 15 * 32 = 480; y = 480/12 = 40.

Front

What is the graphical representation of inverse variation?

Back

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

Front

Can inverse variation be represented by a linear equation?

Back

No, inverse variation is not linear; it is represented by a hyperbolic curve.