Ants have two legs. elena znd andre write equations showing the proportional relationship between the number of ants, a, to the number of ant legs l. elena writes a = 6• l and andre writes l = 1\6 • a. do you agree with either one of the equations? expain your reasoning.

 Yes, I do agree with both the equations.

Step-by-step explanation: It is given that ants have two legs. There is a proportional relationship between the number of ants 'a' and the number of ant's legs 'l'.

So, the can write the proportionality relationship as follows -

a ∝ l.

Obviously, this can be replaced by a similar relation

where 'k' is a constant of proportionality.

Since 'k' is any constant, so its value may be 6, because it is also a constant.

Then, we can have

Thus, both the equations are correct.

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!