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

How do you find the constant of variation (k) in a direct variation problem?

Back

To find the constant of variation (k), divide the value of y by the corresponding value of x (k = y/x).

Front

If y varies directly as x and y = 18 when x = 3, what is the constant of variation (k)?

Back

k = y/x = 18/3 = 6.

Front

What is the equation of direct variation when k = 4?

Back

The equation is y = 4x.

Front

If y = -27 when x = 9, what is the value of k?

Back

k = y/x = -27/9 = -3.

Front

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

Back

Use the equation y = kx, substituting the known value of x and the constant k.

Front

If y = 12 when x = 6, what is the value of y when x = 18?

Back

y = kx; first find k: k = 12/6 = 2. Then, y = 2 * 18 = 36.

Front

What is the graphical representation of direct variation?

Back

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

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.

Front

What is the relationship between x and y in direct variation?

Back

In direct variation, as one variable increases, the other variable also increases, and as one decreases, the other decreases.