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 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

Identify the equation for Direct Variation.

Back

The equation for Direct Variation is y = kx.

Front

Identify the equation for Inverse Variation.

Back

The equation for Inverse Variation is y = k/x.

Front

What does the constant 'k' represent in Direct Variation?

Back

In Direct Variation, 'k' represents the constant of variation, which indicates how much y changes for a unit change in x.

Front

What does the constant 'k' represent in Inverse Variation?

Back

In Inverse Variation, 'k' represents the constant of variation, which indicates the product of x and y remains constant.

Front

If y varies directly with x, and y = 10 when x = 2, what is the value of k?

Back

k = 5, since y = kx implies 10 = k(2) => k = 10/2 = 5.

Front

If y varies inversely with x, and y = 4 when x = 3, what is the value of k?

Back

k = 12, since y = k/x implies 4 = k/3 => k = 4 * 3 = 12.

Front

What is the graph of Direct Variation?

Back

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

Front

What is the graph of Inverse Variation?

Back

The graph of Inverse Variation is a hyperbola that approaches the axes but never touches them.