Question 30514: I need help with a linear function table. Here's the table:
x f(x)
-6 -15
1 -1
7 11
11 19
I tried to find the pattern for the y's and the x's so that I could find the slope, but it doesn't seem like there is a pattern. I need to write the rule for the linear equation. Can you help?
Thanks
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! you say it is a linear function, so in that case, we are looking for a "times table".
Pick any 2 values of x... say 7 and 11. They differ by 4. Their F(x) values are 11 and 19, which differ by 8.
So, x increases by 4 whilst y increases by 8... looks like the 2 times table to me.
--> f(x) = 2x
Now, it isn't THE 2x table: 2,4,6,8,10,... etc, but it is this shifted.
So, when x=7, f(x)=2x gives f(x)=14. Our function actually gives 11, so we need to subtract 3: f(x)= 2x-3.
CHECK:
when x=-6
f(-6) = 2(-6) - 3
f(-6) = -12 - 3
f(-6) = -15... CORRECT
You can then tell what the slope of the line is from y=2x-3
jon.
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