Find the slope given the following points: (12,-2) and (4,-6)

slope=1/2 or

y=1/2x-8

Step-by-step explanation:

use the y1-y2/x2-x1 method and y=mx+b method

plug in the -2 and -6 into the y's value

then plug in 12 and 4 into the x's value

-2+6=4

12-4=8

4/8 that can reduce to 1/2

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you can plug it into the y=mx+b method

plug in 12 for x

-2 for y

and 1/2 for m

-2=1/2(12)+b

1/2 *12=6

-2=6+b

substract 6 on both sides

-8=b and ur b is ur y-intercept

y=1/2x-8

hope this helps

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!