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

If y is directly proportional to x, what does that mean?

Back

It means that as x increases or decreases, y changes in a consistent manner, maintaining the ratio y/x = k.

Front

What is the constant of variation in direct variation?

Back

The constant of variation (k) is the constant ratio of y to x in the equation y = kx.

Front

How do you find the constant of variation if y = 10 when x = 2?

Back

To find k, use the formula k = y/x. Here, k = 10/2 = 5.

Front

If y = 5 when x = 1, what is y when x = 4?

Back

Using the constant of variation k = 5, y = kx = 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

If y varies directly with x and y = 12 when x = 3, what is the equation?

Back

The equation is y = 4x, since k = 12/3 = 4.

Front

How do you determine if a graph represents direct variation?

Back

A graph represents direct variation if it is a straight line that passes through the origin.

Front

If y = 2x and x = 5, what is y?

Back

y = 2 * 5 = 10.

Front

What happens to y if x is doubled in a direct variation?

Back

If x is doubled, y will also double, maintaining the direct proportionality.