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 formula for Direct Variation?

Back

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

Front

If y varies directly with x, what happens to y when x is multiplied by a factor?

Back

If x is multiplied by a factor, y is also multiplied by the same factor.

Front

What is the constant of variation in the equation y = 3x?

Back

The constant of variation is 3.

Front

How can you determine if a set of points represents a direct variation?

Back

A set of points represents a direct variation if the ratio of y to x is constant for all points.

Front

Is the relationship between x and y in the equation y = 2x + 1 a direct variation?

Back

No, it is not a direct variation because of the +1; direct variation must pass through the origin.

Front

What does a graph of a direct variation look like?

Back

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

Front

If x = 4 and y = 12, what is the constant of variation k?

Back

k = y/x = 12/4 = 3.

Front

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

Back

y = kx; k = 10/2 = 5; y = 5 * 5 = 25.

Front

Which of the following equations represents a direct variation: y = 4x, y = x^2, y = 3 + 2x?

Back

y = 4x represents a direct variation.