Direct 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 proportionality?

Back

The constant of proportionality is the constant factor (k) in the direct variation equation y = kx. It represents the ratio of y to x.

Front

Write an equation for a direct variation where the constant of proportionality is 5.

Back

y = 5x

Front

If y = 3x, what is the constant of proportionality?

Back

3

Front

Which of the following represents a direct variation: y = 2x + 3 or y = 4x?

Back

y = 4x (because it does not have a constant term added).

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

If y varies directly with x and y = 12 when x = 4, what is the constant of proportionality?

Back

3 (because k = y/x = 12/4).

Front

Write an equation for a direct variation where y = 10 when x = 2.

Back

y = 5x (because k = 10/2 = 5).

Front

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

Back

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

Front

If the constant of proportionality is 8, what is y when x = 3?

Back

24 (because y = 8 * 3).