Direct & Inverse Variation Unit Review

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 as x and y = 3 when x = 12, what is the constant of variation (k)?

Back

k = y/x = 3/12 = 1/4.

Front

If y = -20/x, what is the value of y when x = 4?

Back

y = -20/4 = -5.

Front

What does the graph of a direct variation look like?

Back

The graph of a direct variation is a straight line that passes through the origin (0,0).

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

If y = -rac{2}{5}x, is this a direct or inverse variation?

Back

This is a direct variation.

Front

If y varies inversely as x and y = 10 when x = 2, what is the value of y when x = 5?

Back

k = yx = 10*2 = 20; y = 20/5 = 4.

Front

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

Back

In direct variation, as x increases, y also increases, and as x decreases, y also decreases.

Front

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

Back

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