Direct & Inverse Flashcard

Front

What is a direct variation?

Back

A 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 an inverse variation?

Back

An inverse variation is a relationship between two variables where the product of the two variables is a constant. It can be expressed as y = k/x, where k is a non-zero constant.

Front

If y varies directly as x, and y = -7 when x = -14, what is the constant of variation (k)?

Back

k = y/x = -7 / -14 = 0.5.

Front

If y varies directly as x, and k = 0.5, what is y when x = 20?

Back

y = kx = 0.5 * 20 = 10.

Front

If y varies inversely as x, and y = 4 when x = 7, what is the constant of variation (k)?

Back

k = xy = 7 * 4 = 28.

Front

If y varies inversely as x, and k = 28, what is y when x = 2?

Back

y = k/x = 28/2 = 14.

Front

Trina's paycheck earnings varies directly as the number of hours she works. If she works 19 hours and earns $187.15, what is her hourly wage?

Back

Hourly wage = Total earnings / Hours worked = 187.15 / 19 = $9.85.

Front

If 8 books cost $10.40, what is the cost per book?

Back

Cost per book = Total cost / Number of books = 10.40 / 8 = $1.30.

Front

If the cost of books is $1.30 per book, how many books can be bought for $32.50?

Back

Number of books = Total money / Cost per book = 32.50 / 1.30 = 25 books.

Front

What is the formula for direct variation?

Back

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