The variables a and b vary directly, and b=8 when a=2. What is the direct variation equation that relates a and b?

A.

b=2a.

B.

b-4a

C

b=8a

D

b=16a

b= 4a

( This is the correct answer, which is supposed to be option b, but a negative sign was put instead of an equal sign, so you can change appropriately)  

Step-by-step explanation:

Given that a and b vary directly, can be expressed as

a ∝ b

Introducing the constant of proportionality, k, we have that

a = kb

so when a= 2, b= 8 and the constant becomes

2 = k8

k = 2/8=1/ 4

a= 1/4b

Such that

b=4a

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

okay wait before i answer, is this for your points on a graph?