5.
(05.02 lc)
which equation does the graph below represent?

y = x

y = –3x

y = 3x

y = x

y = -3x

Step-by-step explanation:

Given the illustration of the graph, we can see that the line is going downhill.  This would indicate that the slope is negative, so the choices would be narrowed down y = -3x or y = -x.  Looking at the line, we can use two points to find the difference in 'y' over the difference in 'x', or slope.  Using the origin (0,0) as one point, we can go down 3 and over 1 to get to the second point of (1, -3).  This would be an overall change of -3, giving us the final answer of:

y = -3x

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!