Direct variation

Front

What is a direct variation?

Back

A direct variation is a proportional linear relationship between two variables, where one variable is a constant multiple of the other.

Front

If y varies directly as x, what is the equation form?

Back

y = kx, where k is the constant of variation.

Front

What does the constant of variation (k) represent in direct variation?

Back

The constant of variation (k) represents the scale factor that relates y to x.

Front

Which equation represents a direct variation with a scale factor of 5?

Back

y = 5x.

Front

If y = 10 when x = 2, what is the constant of variation (k)?

Back

k = 10/2 = 5.

Front

If y = 15 when x = 3, what is the value of y when x = 4?

Back

y = 5 * 4 = 20.

Front

What is the graph of a direct variation?

Back

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

Front

How can you tell if a table of values represents a direct variation?

Back

If the ratio of y to x is constant for all pairs of values, it represents a direct variation.

Front

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

Back

As x increases, y increases proportionally, and as x decreases, y decreases proportionally.

Front

If y = 12 when x = 4, what is y when x = 6?

Back

y = (12/4) * 6 = 18.