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Question
hi im not sure how to find the rule for a function table

x=1, 2, 3, 4
y=9,27,45,63


Y=?x-?
that is the linear equation but i don't know how to fill in the question marks

Answer
Hi Brittany,
Since the relationship is linear, you can take any two sets of points to model the linear line
y = mx + c
where m = Δy/Δx
If we take x=1,y=9 and x=2,y=27
m = (27 - 9)/(2 - 1)
= 18
So,
y = 18x + c
and you can find c using any of the points, say, x=1,y=9
9 = 18(1) + c
9 = 18 + c
c = -9
Therefore,
y = 18x - 9

Another way to do this is to consider the y sequence as a linear progression with first term 9 and common difference 18, and so
y = 9 + (x-1).18
= 9 + (18x - 18)
= 18x - 9

Regards

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