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anonymous
 one year ago
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^28
C.) 6x8
Thank you!! <3
anonymous
 one year ago
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^28 C.) 6x8 Thank you!! <3

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1You can think of it as of a sequence. lets figure out the pattern. \(\large\color{black}{ \displaystyle {\rm d}={\rm a}_{n}{\rm a}_{n1} }\) 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
 one year ago
Best ResponseYou've already chosen the best response.1So 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
 one year ago
Best ResponseYou've already chosen the best response.1So you have a slope of 6, and (lets choose) a point (0, 8)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Now, 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
 one year ago
Best ResponseYou've already chosen the best response.0so it would be 6x8, then?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, that is correct:)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yay! you are so helpful. :)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You are awesome. :))
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