The school enrollment for oakwood elementary is shown in the graph. if the pattern continues, what will the school enrollment be in 2012? question 19 options: 500 525 550 575

Option B. 525 students.

Step-by-step explanation:

The school enrollment for Oakwood Elementary is shown in the graph.

The given graph is representing a linear function. So we will form the function first to calculate the enrollment in 2012.

Equation of the given line in the graph will be in the form of y = mx + c

where m is the slope and c = y- intercept

y-intercept = 300

this line passes through two ordered pairs (0, 300) and (1, 325)

Now the slope m =

m =

Therefore, equation representing the situation will be y = 25x + 300

Now we will put the value of x = year 2012 - year 2003 = 9 years

y = 25×9 + 300

y = 225 + 300

y = 525

Option B. 525 is the correct option.

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!