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 constant of variation in direct variation?

Back

The constant of variation (k) is the constant ratio of y to x in a direct variation equation, represented as k = y/x.

Front

If y varies directly with x and k = 5, what is the equation?

Back

The equation is y = 5x.

Front

In a direct variation, if y = 20 when x = 4, what is the constant of variation?

Back

The constant of variation k = y/x = 20/4 = 5.

Front

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

Back

To find y, use the equation y = kx, substituting the value of k and the given x.

Front

If y = 12 when x = 3, what is y when x = 6 in a direct variation?

Back

y = 12 when x = 3, so k = 12/3 = 4. When x = 6, y = 4 * 6 = 24.

Front

Is the relationship y = 2x + 3 a direct variation?

Back

No, because direct variation must be in the form y = kx, without any additional constants.

Front

What does it mean if y varies directly with x?

Back

It means that as x increases or decreases, y changes in direct proportion to x.

Front

If y = 15 when x = 5, what is y when x = 10?

Back

k = 15/5 = 3. Therefore, y = 3 * 10 = 30.

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).