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, typically expressed as y = kx, where k is a non-zero constant.

Front

What is the constant of variation in direct variation?

Back

The constant of variation (k) is the constant factor that relates the two variables in a direct variation equation.

Front

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

Back

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

Front

What is the general form of a direct variation equation?

Back

The general form is y = kx, where k is the constant of variation.

Front

How do you find the value of y when x is given in a direct variation?

Back

Substitute the value of x into the equation y = kx, using the known value of k.

Front

What ordered pair does a direct variation always pass through?

Back

(0, 0) because when x = 0, y must also be 0.

Front

If y = 3 when x = 1, what is the equation of the direct variation?

Back

y = 3x.

Front

How can you determine if a relationship is a direct variation?

Back

If the ratio of y to x is constant for all pairs of values, then the relationship is a direct variation.

Front

What is the relationship between the graphs of direct variation and linear equations?

Back

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

Front

If y = 12 when x = 4, what is the value of y when x = 10?

Back

First find k: k = y/x = 12/4 = 3. Then, y = kx = 3 * 10 = 30.