A bowling alley charges $3.50 each game in addition to $8 for shoes. What is the equation the represents y, the total cost for bowling for x games?

In this question, we have to make an equation with the given scenario.

We can make an equation using slope intercept form:

y = mx + b

Whereas:

y = total cost

x = amount of games

We know that the bowling alley charges $3.50 for EACH game

So we can represent that with our "m" variable, it would be: 3.50x

Our equation as of right now:

y = 3.50x + b

We also know that the bowling alley charges a one-time payment of $8 for shoes, so that would be our "b" variable.

Plug 8 into the b value:

y= 3.50x + 8

y= 3.50x + 8

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!

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363