Question

Which of the following ordered pairs could be placed in the table and still have the relation qualify as a linear function?

Input (x)
Output (y)

1 12
3 9
5 6
? ?

(7, 3)
(7, 10)
(3, 3)
(3, 10)

Answer 1

Your answer would be A (7,3)

Answer 2

linear functions have to have the same slope between any 2 points

find the slope betwen them
slope betwen 2 points (x1,y1) and (x2,y2) is
(y1-y1)/(x2-x1)
given
(1,12) and (3,9)
slope=(9-12)/(3-1)=-3/2

if we wanted to chek furthere, we check (3,9) and (5,6) and fnd that the slope is also -3/2

so
y=mx+b
m=slope
b=yint
y=-3/2x+b
find b
if x=1 then y=12
12=-3/2+b
add 3/2 both sides
12+3/2=b
13+1/2=b
26/2+1/2=b
27/2=b
y=-3/2x+27/2
try them

we have 2 x values
7 and 3
input them and see their outputs

for x=7
y=-3/2(7)+27/2
y=-21/2+27/2
y=6/2
y=3
(7,3) is a valid point

for x=3
hold a second, we already have a x=3
it is (3,9)
none of them


answer is (7,3)