anonymous
  • anonymous
In this table, the input and output values are related. If you know the input, you can predict the output. Which rule describes how the output depends on x? |Input | Output| | 0 | -8 | | 1 | -2 | | 2 | 4 | | 3 | 10 | A.) -8x+6 B.) 6x^2-8 C.) 6x-8 Thank you!! <3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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SolomonZelman
  • SolomonZelman
You can think of it as of a sequence. lets figure out the pattern. \(\large\color{black}{ \displaystyle {\rm d}={\rm a}_{n}-{\rm a}_{n-1} }\) such that: \(\large\color{black}{ \displaystyle {\rm d}={\rm a}_{2}-{\rm a}_{1} }\) (for n=2) \(\large\color{black}{ \displaystyle {\rm d}={\rm a}_{3}-{\rm a}_{2} }\) (for n=3) \(\large\color{black}{ \displaystyle {\rm d}={\rm a}_{4}-{\rm a}_{3} }\) (for n=4) and etc., Now I will plug in some terms. \(\large\color{black}{ \displaystyle (-8)-(-2)=-8+2=-6 }\) \(\large\color{black}{ \displaystyle (-2)-(4)=-6 }\) \(\large\color{black}{ \displaystyle (4)-(10)=-6 }\)
SolomonZelman
  • SolomonZelman
So you can see that the "common difference" here (or the number you add to get from one term to the next) is -6, and that is your slope (since difference of -6 is wlays same as I showed)
SolomonZelman
  • SolomonZelman
So you have a slope of -6, and (lets choose) a point (0, -8)

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SolomonZelman
  • SolomonZelman
Now, we can use a point slope form: \(\large\color{black}{ \displaystyle {\rm y}- {\rm y}_1={\rm m}\left( {\rm x}- {\rm x}_1\right) }\) go for it...
anonymous
  • anonymous
so it would be 6x-8, then?
anonymous
  • anonymous
wait let me check
SolomonZelman
  • SolomonZelman
yes, that is correct:)
anonymous
  • anonymous
yay! you are so helpful. :)
SolomonZelman
  • SolomonZelman
I mean, you can right away exclude other options as soon as you see that the difference is same. because the fact that difference is same indicates that the function is linear (in a form of y=mx+b), and only C is a linear function.
SolomonZelman
  • SolomonZelman
yw
anonymous
  • anonymous
You are awesome. :))
SolomonZelman
  • SolomonZelman
Thank you!

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