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

If y varies directly with x, what does that imply about their relationship?

Back

It implies that as x increases or decreases, y will increase or decrease proportionally, maintaining a constant ratio.

Front

What is the formula for Direct Variation?

Back

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

Front

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

Back

You can find k by rearranging the formula to k = y/x using known values of x and y.

Front

If y = 12 when x = 15, what is the constant of variation (k)?

Back

k = 12/15 = 0.8.

Front

If y = 15 when x = 3, what is the value of y when x = 7?

Back

y = kx = (15/3) * 7 = 35.

Front

If y = -27 when x = 9, what is the value of y when x = 20?

Back

y = kx = (-27/9) * 20 = -60.

Front

If y varies directly with x and y = 16 when x = 20, what is the value of x when y = 12?

Back

x = (12/16) * 20 = 15.

Front

How do you solve a direct variation problem?

Back

1. Identify the known values of x and y. 2. Find the constant k. 3. Use the formula y = kx to find the unknown.

Front

What is the relationship between the number of packages and pieces of Starburst if they vary directly?

Back

If the number of pieces varies directly with the number of packages, then the ratio of pieces to packages remains constant.