Direct Variation

Objectives

• To learn what direct variation is

• To solve problems using direct variation

• To solve real-life problems using direct variation

What is Direct Variation?

• Direct variation means that in an equation, one term is multiplied by a constant to get the other term.

• If k is the constant, the formula is written y = kx.

• For example, in the equation y = 4x, 4 is the constant. If x is 2, y is 8. If x is -6, y is -24.

What is Direct Variation?

• Direct variation also means that the variables are proportional.

• Example: Y varies directly with x. When x is 4 y is 20, when y is -10, what is x?

20

4

-10x -40=20x

20 20x = -2

Direct Variation Examples

• Y varies directly with x. When x is 3, y is 10.5. When x is 7, what is y?

• H varies directly with p. When h is 9, p is 13. When p is 8, what is h?

5.10

3

y7 3y = 73.5

3 3y = 24.5

13

9

8h 13h = 72

13 13h ≈ ?

Direct Variation Examples

• X varies directly with Y. When x is 42, y is -6. When x is 21, what is y?

• w varies directly with x. When w is 2, x is 28. When w is 7, what is x?

6

42

y21 42y = -126

42 42y = ?

28

2

x7 2x = 196

2 2x = ?

Direct Variation Word Problems

• The shadow of an object varies directly with its height. The shadow of a 25 ft object is 6 ft. How long is the shadow of an 18 ft tree?

6

25

s18 25s = 108

25 25s = 4.32

The shadow of the tree is

4.32 ft.

Direct Variation Word Problems

• The circumference of a circle varies directly with the diameter. The diameter of a circle is 6 in and the circumference is 18.84 in. If the circumference of a circle is 25 ft, what is the diameter to the nearest hundredth?

84.18

6

25d 150 = 18.84d

18.84 18.84d = 7.96

The diameter is 7.96 ft.

Direct Variation Word Problems

• The number of potatoes harvested varies directly with the area of the garden. If 200 potatoes are harvested from 10 square feet, how many potatoes would be harvested from 45 square feet?

10

200

45p 9000 = 10p

10 10p = 900

900 potatoes could be harvest in 45 ft2.