Do the following scenarios model the equation y=2x+5 there are initially 5 chickens on the farm. each month thereafter the number of chickens is 2 times the number in the month before

 Yes, the given scenarios model the equation

Step-by-step explanation:  The given linear equation is

Let x represents the number of months and y represents the corresponding number of chickens after x months on the firm.

Given that there are initially 5 chickens on the firm, so we have

when x = 0, then y = 5.

Also, since each month thereafter the number of chickens is 2 times the number in the month before, so

when x = 1, y = 5 + 2 = 7,

when x = 2, y = 7 + 2 = 9,

when x = 3, y = 9 + 2 = 11, etc.

So, (x, y) = (0, 5), (1, 7), (2, 9), (3, 11), etc. are points lying on the linear function described by x and y.

The slope of the line passing through the points (0, 5) and (1, 7) will be given by

Therefore, the equation of the line is

Since the above equation is same as equation (i), so the answer is YES.

The given scenario model the equation

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!