9.5 = Variation Functions.

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Presentation transcript:

9.5 = Variation Functions

Direct Variation

Direct Variation – y varies directly as x

Direct Variation – y varies directly as x y = kx

Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #)

Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation

Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation – y varies inversely as x

Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation – y varies inversely as x y = k x

Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation – y varies inversely as x y = k x Joint Variation

Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation – y varies inversely as x y = k x Joint Variation – y varies jointly as x and z

Direct Variation – y varies directly as x y = kx *Note: k = constant of variation (a #) Inverse Variation – y varies inversely as x y = k x Joint Variation – y varies jointly as x and z y = kxz

Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation.

Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20

Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20

Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 a

Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse a

Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a

Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y = -0.5 x

Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y = -0.5 x y = -0.5x

Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y = -0.5 x y = -0.5x , direct

Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y = -0.5 x y = -0.5x , direct, k = -0.5

Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y = -0.5 x y = -0.5x , direct, k = -0.5 c. A = ½bh

Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y = -0.5 x y = -0.5x , direct, k = -0.5 c. A = ½bh , joint

Ex. 1 State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. a. ab = 20 b = 20 , inverse, k = 20 a b. y = -0.5 x y = -0.5x , direct, k = -0.5 c. A = ½bh , joint , k = ½

Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20.

Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20.

Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx

Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx

Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 18 = k(15)

Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 18 = k(15) 18 = 15k

Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 18 = k(15) 18 = 15k 18 = k 15

Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 18 = k(15) 18 = 15k 18 = k 15 6 = k 5

Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 2) y = kx 18 = k(15) 18 = 15k 18 = k 15 6 = k 5

Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 2) y = kx 18 = k(15) y = 6x 18 = 15k 5 18 = k 15 6 = k 5

Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 2) y = kx 18 = k(15) y = 6x 18 = 15k 5 18 = k 15 6 = k 5

Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 2) y = kx 18 = k(15) y = 6x 18 = 15k 5 18 = k y = 6(20) 15 5 6 = k 5

Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 2) y = kx 18 = k(15) y = 6x 18 = 15k 5 18 = k y = 6(20) 15 5 6 = k y = 120 5 5

Ex. 2 Find each value. a. If y varies directly as x and y = 18 when x = 15, find y when x = 20. 1) y = kx 2) y = kx 18 = k(15) y = 6x 18 = 15k 5 18 = k y = 6(20) 15 5 6 = k y = 120 5 5 y = 24

Suppose y varies jointly as x and z Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6

Suppose y varies jointly as x and z Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 1) y = kxz

Suppose y varies jointly as x and z Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 1) y = kxz -90 = -6(15)k

Suppose y varies jointly as x and z Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 1) y = kxz -90 = -6(15)k -90 = -90k

Suppose y varies jointly as x and z Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k

Suppose y varies jointly as x and z Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz

Suppose y varies jointly as x and z Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz y = 1xz

Suppose y varies jointly as x and z Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz y = 1xz y = 1(9)(-5)

Suppose y varies jointly as x and z Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz y = 1xz y = 1(9)(-5) y = -45 If y varies inversely as x and y = -14 when x = 12, find x when y = 21

If y varies inversely as x and y = -14 when x = 12, find x when y = 21 Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz y = 1xz y = 1(9)(-5) y = -45 If y varies inversely as x and y = -14 when x = 12, find x when y = 21 1) y = k x -14 = k 12 -168 = k

If y varies inversely as x and y = -14 when x = 12, find x when y = 21 Suppose y varies jointly as x and z. Find y when x = 9 and z = -5, if y = -90 when z = 15 and x = -6 1) y = kxz -90 = -6(15)k -90 = -90k 1 = k 2) y = kxz y = 1xz y = 1(9)(-5) y = -45 If y varies inversely as x and y = -14 when x = 12, find x when y = 21 1) y = k x -14 = k 12 -168 = k 2) y = k x 21 = -168 x = -8