An equation of the line passing through the points (4,3) and (-1,1)

A = ( 4 , 3 ) ..**&**.. B = ( - 1 , 1 )

Slope = [ y(B) - y(A) ] ÷ [ x(B) - x(A) ]

Slope = [ 1 - 3 ] ÷ [ - 1 - 4 ]

Slope = [ - 2 ] ÷ [ - 5 ]

Slope = 2/5

y - y(0) = Slope × ( x - x(0) )

y - y(A) = Slope × ( x - x(A) )

y - 3 = 2/5 × ( x - 4 )

y - 3 = 2/5 x - 8/5

y = 2/5 x - 8/5 + 3

y = 2/5 x - 8/5 + 15/5

y = 2/5 x + 7/5

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!

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x