Question

Do the data in the table represent a direct variation or an inverse variation? write an equation to model the data in the table.

x 1 2 5 10

y 40 20 8 4

a. Direct variation; y=40x
b. Direct variation; y=(1/40)x
c. Inverse variation; xy=40
d. Inverse variation; xy=1/40

I feel so stupid for not knowing the answer, please explain it to me.

Answer 1

x = 1, 2, 5, 10
y = 40,20, 8, 4

a) y = 40x
y = 40(1) = 40 ; y = 40(2) = 80 ;
y = 40(5) = 200 ; y = 40(10) = 400

b) y = (1/40)x ;
y = (1/40)1 = 1/40 ; y = (1/40)2 = 1/20 ;
y = (1/40)5 = 1/8 ; y =(1/40)10 = 1/4

c) xy = 40 ⇒ y = 40/x
y = 40/1 = 40 ; y = 40/2 = 20
y = 40/5 = 8 ; y = 40/10 = 4

Inverse variation. Choice C. xy = 40 is the correct answer.