Algebra Flashcard: 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 a non-zero constant.

Front

What is the equation form of direct variation?

Back

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

Front

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

Back

A direct variation can be identified if the ratio of y to x (y/x) is constant for all pairs of values.

Front

What does the constant of variation represent in direct variation?

Back

The constant of variation (k) represents the factor by which y changes for a change in x.

Front

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

Back

The constant of variation is 3.

Front

Is the relationship y = 2x + 1 a direct variation?

Back

No, because it includes a constant term (1) which makes it non-proportional.

Front

What is the constant of variation for the equation y = -5x?

Back

The constant of variation is -5.

Front

If a table shows the values (2, 6), (4, 12), (6, 18), is this a direct variation?

Back

Yes, because the ratio y/x is constant (3 in this case).

Front

What is the relationship between direct variation and proportionality?

Back

Direct variation is a type of proportional relationship where the ratio of y to x is constant.

Front

If y = 0.5x, what is the constant of variation?

Back

The constant of variation is 0.5.