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 does the letter k represent in the equation y = kx?

Back

The letter k represents the constant of proportionality in the equation y = kx.

Front

True or False: An equation of direct variation can be written in the form y = kx.

Back

True

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 = 3x, is this a direct variation?

Back

Yes, this is a direct variation because it can be expressed in the form y = kx, where k = 3.

Front

If y = 2x + 1, is this a direct variation?

Back

No, this is not a direct variation because it does not pass through the origin.

Front

What is the constant of proportionality in the equation y = 5x?

Back

The constant of proportionality is 5.

Front

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

Back

k = 5, because y = kx implies 10 = k(2).

Front

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

Back

y = 4x represents a direct variation.

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.