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 does the constant k represent in Direct Variation?

Back

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

Front

If y varies directly with x and y = 12 when x = 3, what is the value of k?

Back

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

Front

If y varies directly with x, and y = 20 when x = 5, what is y when x = 10?

Back

y = kx = 4 * 10 = 40.

Front

If y varies directly with x, and y = -30 when x = 6, what is y when x = -12?

Back

y = kx = -5 * -12 = 60.

Front

If y varies directly with x, and y = 0 when x = 0, what can we conclude?

Back

If y = 0 when x = 0, it confirms that the relationship is consistent with direct variation.

Front

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

Back

To find x, rearrange the direct variation equation y = kx to x = y/k.

Front

If y varies directly with x, and y = 15 when x = 3, what is x when y = 45?

Back

x = y/k = 45/5 = 9.

Front

If y varies directly with x, and y = -24 when x = 8, what is y when x = -16?

Back

y = kx = -3 * -16 = 48.

Front

What is the formula for Direct Variation?

Back

The formula for Direct Variation is y = kx.