Exponent Laws and Inverse Variation Practice

Front

What is inverse variation?

Back

Inverse variation is a relationship between two variables in which the product of the variables is constant. If one variable increases, the other decreases.

Front

What is the constant of inverse variation?

Back

The constant of inverse variation (k) is the product of the two variables in an inverse relationship, represented as k = xy.

Front

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

Back

If the product of the paired values remains constant across the table, then the relationship is an inverse variation.

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where they increase or decrease together, represented as y = kx, where k is a constant.

Front

How do you find the constant of proportionality in direct variation?

Back

The constant of proportionality (k) in direct variation can be found by dividing y by x (k = y/x).

Front

What does a graph of inverse variation look like?

Back

A graph of inverse variation typically shows a hyperbola, where as one variable increases, the other decreases.

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, indicating a constant ratio between the variables.

Front

If y varies inversely with x, and y = 12 when x = 4, what is the constant k?

Back

k = xy = 12 * 4 = 48.

Front

If the table shows values (2, 24), (3, 16), (4, 12), does it represent inverse variation?

Back

Yes, because the product of each pair (2*24, 3*16, 4*12) equals 48.

Front

What is the relationship between speed and time in inverse variation?

Back

As speed increases, time decreases for a constant distance, illustrating inverse variation.