Direct Variation Practice

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, typically expressed in the form y = kx, where k is a non-zero constant.

Front

What does the constant k represent in direct variation?

Back

The constant k represents the constant of variation, which indicates how much y changes for a unit change in x.

Front

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

Back

k = y/x = 10/2 = 5.

Front

What is the general form of a direct variation equation?

Back

The general form of a direct variation equation is y = kx.

Front

What ordered pair does a direct variation always pass through?

Back

A direct variation always passes through the origin, represented by the ordered pair (0, 0).

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

If y = 3x and x = 4, what is the value of y?

Back

y = 3(4) = 12.

Front

What is the relationship between x and y in the equation y = 2x + 3?

Back

This equation does not represent direct variation because it does not pass through the origin; it has a y-intercept of 3.

Front

If y varies directly with x and y = 15 when x = 5, what is the equation of the direct variation?

Back

The equation is y = 3x.

Front

In a direct variation, if x is doubled, what happens to y?

Back

If x is doubled, y is also doubled, since y varies directly with x.