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 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 the constant of variation.

Front

How do you determine if a table represents Direct Variation?

Back

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

Front

How do you determine if a table represents Inverse Variation?

Back

A table represents inverse variation if the product of x and y is constant for all pairs of values.

Front

What is the constant of variation in Direct Variation?

Back

The constant of variation in direct variation is the ratio k, which can be found by dividing y by x (k = y/x).

Front

What is the constant of variation in Inverse Variation?

Back

The constant of variation in inverse variation is the product k, which can be found by multiplying x and y (k = xy).

Front

If y varies directly as x and y = 10 when x = 2, what is y when x = 5?

Back

y = 25.

Front

If y varies inversely as x and y = 6 when x = 3, what is y when x = 1?

Back

y = 18.

Front

What does a graph of Direct Variation look like?

Back

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

Front

What does a graph of Inverse Variation look like?

Back

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