Inverse Variation

What kind of variation does the two quantities shown in the given situation?

The time the painter paints a wall is related to the area of the wall painted?

• Direct Variation

• Inverse variation

Answer explanation

The more time a painter spends painting a wall, the greater the area of the wall that is painted.

What kind of variation does the two quantities show?

The age of used car is related to the price the owner can get for it.

• Direct variation

• Inverse Variation

Answer explanation

As the age of the used car increases, the price of the owner can get for it decreases.

The number of people sharing a pizza is related to the size of the slice each person gets is an example of inverse variation. Type the explanation or the statement showing these quantities are inversely proportional to one another.

Example : As the number of people ________, .....

Which of the following graphs show an inverse relationship between x and y?

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The length of time a car travels varies inversely as its speed. Let t=length of time, r=speed, and k= constant of variation. What equation relates t and r?

Answer explanation

The equation for inverse variation is y=k/x.

y varies inversely as x such that when x=12, y=9. Find y when x=27.

• 3

• 4

• 9

• 18

Answer explanation

First determine the value of k using the equation y=k/x. To solve for k, multiply the values of x and y, that is k=(12)(9) which is equal to 108. Then substitute in the equation y=k/x, that is y=108/27 and the answer is 4.

The length of time a bag of cat food lasts varies inversely with the number of cats. If the bag of cat food will feed 5 cats for 10 days, how long will it feed 10 cats?

• 50 days

• 5 days

• 1/2 day

• 1

Answer explanation

You have to find first the k using the equation k=xy. The number of cats is x and the number of days is y. When you multiply x and y, you will get 50 as the value for k. To get the number of day, use the equation y=k/x and substitute the values, thus y=50/10=5 days.

y varies inversely as x. When x=2, y= 1/2, find y when x=1/8.

• 1

• 1/8

• 8

• 4

What kind of variation does the two quantities shown in the given situation?

The time the painter paints a wall is related to the area of the wall painted?

• Direct Variation

• Inverse variation

Answer explanation

The more time a painter spends painting a wall, the greater the area of the wall that is painted.