SOLUTION: Find the rule for this table S T _ 70 _ 66 9 62 12 58 15 54

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Question 1125283: Find the rule for this table
S T
_ 70
_ 66
9 62
12 58
15 54
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
S+|+++T
_+|+++70
_|+++++66
9+|++++62
12+|++58
15|++++54

first find equation using two of given pairs
T=mS%2Bb...plug in S=9+|+++T=+62
62=9m%2Bb...solve for b
b=62-9m....eq.1

T=mS%2Bb...plug in S=12+|+++T=+58
58=12m%2Bb...solve for b
b=58-12m....eq.2
since let sides of eq.1 and eq.2 are same, equal right sides

62-9m=58-12m.......solve or m
12m-9m=58-62
3m=-4
m=-4%2F3

now find b

b=62-9m....eq.1
b=62-9%28-4%2F3%29
b=62-cross%289%293%28-4%2Fcross%283%29%29
b=62-3%28-4%29
b=62%2B12
b=74

so, your equation is: T=-%284%2F3%29S%2B74

ind missing numbers in the table:
S+|+++T....->70=-%284%2F3%29S%2B74->%284%2F3%29S=74-70->%284%2F3%29S=4->S=4%2F%284%2F3%29->S=3
3+|+++70
6|+++++66....->66=-%284%2F3%29S%2B74->%284%2F3%29S=74-66->%284%2F3%29S=8->S=8%2F%284%2F3%29->S=6
9+|++++62
12+|++58
15|++++54