Direct and 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 the constant of variation.

Front

What is the constant of variation in direct variation?

Back

The constant of variation (k) is the non-zero constant that relates the two variables in a direct variation equation.

Front

How can you identify a direct variation from a table of values?

Back

A table represents direct variation if the ratio of y to x is constant for all pairs of values.

Front

What is inverse variation?

Back

Inverse variation is a relationship where one variable increases as the other decreases. It can be expressed as y = k/x, where k is a non-zero constant.

Front

How do you find the constant of variation in inverse variation?

Back

In inverse variation, the constant of variation (k) can be found by multiplying the two variables together (xy = k).

Front

What is the equation for inverse variation if the width of a rectangle is 6 when the length is 24?

Back

The equation is y = 144/x.

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 varies directly with x, what happens to y if x is doubled?

Back

If x is doubled, y also doubles.

Front

If y varies inversely with x, what happens to y if x is doubled?

Back

If x is doubled, y is halved.