Which equation has a slope of –52 and a y-intercept of –2? A. –5x – 2y = –4
B. –5x – 2y = 4
C. 5x + 2y = 4
D. 5x + 2y = –4

I'm sure there might be a typo in the question (AKA the slope is -5/2)

but the answer would be

D

Step-by-step explanation:

y= mx+ b

where m is the slope, and b is the y intercept

y= -52x -2

..........

5x + 2y = –4

2y= -5x -4

y= - 5/2x -2

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!