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:

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