Question

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

Answer 1

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