*PLS HELP* Question:
The quantities x and y are proportional.
Find the constant of proportionality (r) in the equation y = rx
r=(_)

r = 2.5

Step-by-step explanation:

x is directly proportional to y. This can be written as,

x ∝ y

In terms of constant, the proportionality can be written as,

x = ry

Where r is the constant. The table has a set of values for x and y. Let's substitute the values in the first row into the equation with the constant.

10 = r × 4

r =

r = 2.5

Lets check with the second row.

12.5 = r × 5

r =

r = 2.5

Since both sets of values have the same answer for the constant, this means that the third row of values should probably have the same constant.

r = 2.5

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!

step-by-step explanation: