SOLUTION: What is the function rule for this function table:
Input. 0,4,8,12
Output 5,7,9,11
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Question 646229: What is the function rule for this function table:
Input. 0,4,8,12
Output 5,7,9,11
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
What is the function rule for this function table:
Input. 0,4,8,12
Output 5,7,9,11
--------------------
y = mx + b
m = slope = (7-5)/(4-0) = 2/4 = 1/2
b = f(0) = 5
-----
y = (1/2)x + 5
======================
Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Notice that there is a constant difference in the input values from one to the next. There is also a constant difference in the output values form one to the next. Therefore, the relation is linear.
Create two ordered pairs )
using the data given. It doesn't matter which of the pairs 0,5 4,7 8,9 or 12,11 that you pick as long as you have two of them.
Use the two-point form of an equation of a line:
(x\ -\ x_1) )
where )
and )
are the coordinates of the given points.
Do the arithmetic and simplify. Since you are asked for a function rule, you need to solve the equation for 
in terms of everything else. That is, you want to put your equation into slope-intercept form:
That way the function relationship between the 
(Input) values and the (Output) values is clearly established.
John
My calculator said it, I believe it, that settles it
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