Question 9(multiple choice worth 1 points) (4.04 lc) which table of ordered pairs represents a linear function? x y −6 26 0 3 6 26 12 101 x y −6 −3 0 3 6 1 12 2 x y −6 −3 0 3 6 9 6 3 x y −6 −3 0 2 6 7 12 12

we know that

A linear function can be modeled with the equation of a line

We have

case 1

A(-6,26) B(0,3) C(6,26) D(12,101)

Step 1

with point A and B find the equation of a line

Slope m=(y2-y1)/(x2-x1)> m=(3-26)/(0+6)> m=-23/6

with m and point B find the equation of a line

y-y1=m*(x-x1)>y-3=(-23/6)*x> y=(-23/6)x+3

Step 2

check if point C and point D belong to the line

C(6,26) D(12,101)

point C

for x=6 the value of y must be 26

y=(-23/6)*6+3> y=-20

-20 is not equals to 26

so

the ordered pairs of case 1 not represents a linear function

case 2

A(-6,-3) B(0,3) C(6,1) D(12,2)

Step 1

with point A and B find the equation of a line

Slope m=(y2-y1)/(x2-x1)> m=(3+3)/(0+6)> m=1

with m and point B find the equation of a line

y-y1=m*(x-x1)>y-3=(1)*x> y=x+3

Step 2

check if point C and point D belong to the line

C(6,1) D(12,2)

point C

for x=6 the value of y must be 1

y=6+3> y=9

9 is not equals to 1

so

the ordered pairs of case 2 not represents a linear function

case 3

A(-6,-3) B(0,3) C(6,9) D(6,3)

Step 1

with point A and B find the equation of a line

Slope m=(y2-y1)/(x2-x1)> m=(3+3)/(0+6)> m=1

with m and point B find the equation of a line

y-y1=m*(x-x1)>y-3=(1)*x> y=x+3

Step 2

check if point C and point D belong to the line

C(6,9) D(6,3)

point C

for x=6 the value of y must be 9

y=6+3> y=9

9 is equals to 1

point D

for x=6 the value of y must be 3

y=6+3> y=9

9 is not equals to 3

so

the ordered pairs of case 3 not represents a linear function

case 4

A(-6,-3) B(0,2) C(6,7) D(12,12)

Step 1

with point A and B find the equation of a line

Slope m=(y2-y1)/(x2-x1)> m=(2+3)/(0+6)> m=5/6

with m and point B find the equation of a line

y-y1=m*(x-x1)>y-2=(5/6)*x> y=(5/6)x+2

Step 2

check if point C and point D belong to the line

C(6,7) D(12,12)

point C

for x=6 the value of y must be 7

y=(5/6)*6+2> y=7

7 is equals to 7> is ok

point D

for x=12 the value of y must be 12

y=(5/6)*12+2> y=12

12 is equals to 12> is ok

so

the ordered pairs of case 4 represents a linear function

therefore

the answer is

the table xy −6−3 0 2 6 7 12 12 represents a linear function

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!

answer: need picture of problem

step-by-step explanation: