SOS Math 800: Unit 4- Direct Variation

The perimeter of a square is directly proportional to the length of one of its sides. The perimeter is 28 when the length of a side is 7. What is the constant of proportionality?

4

A quantity, y , varies directly as x . When y = 10, x = 6. Find x when y = 14.

8.4

Assume that r varies directly as p . What is the constant of proportionality if r = 3 when p = 15?

k=1/5

The time ( t ) it takes to clean an office building is directly related to the number of people ( p ) working. Which of the following equations can be used to find the constant of variation ( k )?

t/p=k

constant of variation

the rate of change in a direct variation; also known as constant of proportionality

directly proportional

two quantities that increase or decrease (change) by the same factor; also known as directly related

What is the equation of a direct variation that goes through the points (-6, 2) and (9, -3)?

y = -1/3 x

What is the equation of the following direct variation?

y = -2 x

In a direct variation, the constant of proportionality is -3. Which of the following would be its equation?

y = -3 x

The amount that Susan charges per hour for babysitting is directly proportional to the number of children she is watching. She charges $4.50 for 3 kids. How much would she charge to babysit 5 kids?

$7.50

Which of the following sets of points is a direct variation?

(0, 0); (-1, -2); (1, 2)

The relationship between the amount of bleach (in quarts) and the amount of water (in gallons) of a certain cleaning product is a direct variation. The constant of variation is. How much water should be used to dilute 5 quarts of bleach?

15 gallons

The circumference of a circle varies directly as the diameter of a circle. When the diameter of a circle is 5, the circumference of the circle is approximately 15.7. What is the approximate circumference of a circle with a diameter of 9? Round answer to nearest tenth.

28.3

direct variation

a function of the form y = kx, where k is not zero