Direct variation

Front

What is 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 that represents this relationship?

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 ratio of y to x in a direct variation.

Front

If y = 15 when x = 3, what is the constant of variation (k)?

Back

k = y/x = 15/3 = 5.

Front

If y = 5x, what is y when x = 4?

Back

y = 5 * 4 = 20.

Front

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

Back

y = 3x represents a direct variation.

Front

If y varies directly as x and y = 10 when x = 2, what is y when x = 5?

Back

y = (10/2) * 5 = 25.

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

If y = kx, what happens to y if x is doubled?

Back

If x is doubled, y is also doubled, maintaining the direct variation.

Front

What is an example of a real-world situation that can be modeled by direct variation?

Back

The relationship between distance and time at a constant speed is an example of direct variation.