The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:
x g(x)
0 5600
3 5720
6 5840
Part A: Find and interpret the slope of the function (3 points)
Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms (3 points)
Part C Write the equation of the line using function notation. (2 points)
Part D: What is the balance in the bank account after 7 days? (2 points)

A. 4

B. Point-slope: y - 5600 = 40(x-0)

Slope-intercept: y = 40x +5600

Standard: y - 40x = 5600

C. g(x) = 40x + 5600

D. 5880

Step-by-step explanation:

Part A

m = (y2-y1)/(x2-x1)

m = (5720-5600)/(3-0)

m = (120)/(3)

m = 40

Part B

Point-slope: y - 5600 = 40(x-0)

Slope-intercept: y = 40x +5600

Standard: y - 40x = 5600

Part C

g(x) = 40x + 5600

Part D

g(x) = 40(7) + 5600

g(x) = 280 + 5600 = 5880

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!

step-by-step explanation:

1. the cylinder is a. 54

2.   a.108 /