Remmi wrote the equation of the line y=⅓(x+2) he solved for x and got x=3y-2 which of the following is an equivalent equation for x? a. x=y-11/3 b. x=y+7/3 c. x=3(y-⅔) d. x=3(y+⅔)

For this case, we must find an equation equivalent to the given equation, but as a function of y.

If we have:

We must clear "x":

Subtract from both sides of the equation:

We multiply by 3 on both sides of the equation:

Thus, an equivalent equation is:

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!

answer: 94

step-by-step explanation: 79+91+92+94+94 = 450 divided by 5 (since there are 5 number that are being added) = 90