SOLUTION: Hi, I am trying to find the function rule for the following table: x: 2, 4, 6 y: 1, 0, -1. I know that it is x+2 and that the y's are decreasing by 1 each time, but I'm having a

Question 873332: Hi, I am trying to find the function rule for the following table: x: 2, 4, 6 y: 1, 0, -1. I know that it is x+2 and that the y's are decreasing by 1 each time, but I'm having a hard time finding a function rule that works for each x, y pair.
Found 3 solutions by josgarithmetic, richwmiller, rothauserc:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
The slope looks like -1/2, and the x-intercept is 4. Use any form of linear equation that you want to determine corresponding constant value.

USING SLOPE-INTERCEPT FORM

Equation: , which is not showing exactly "x+2".

USING POINT-SLOPE FORM
Any of the given points will work, but x-intercept will be convenient;

, which is equivalent to the other equation found.
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
you have three points
(2,1)
(4,0)
(6,-1)
you have already mentioned the rise -1 (change in y) and the run +2 (change in x)
rise over run = slope
so the slope is -1/2
y=-1/2x+b
0=-1/2*4+b
0=-2+b
b=2
y=-1/2x+2

Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
This a line and note that the standard form for a line is y = mx + b, where m is the slope and b is the y intercept
m = (Y2 - Y1) / (x2 - X1) = (0 - 1) / (4 - 2) = -1/2
so far we have
y = -x/2 + b
let's use the point (4, 0)
0 = -4/2 + b
b = 2
our function is
f(x) = -x/2 + 2

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