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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^2-8 C.) 6x-8 Thank you!! <3

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  1. SolomonZelman
    • one year ago
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    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. \(\large\color{black}{ \displaystyle (-8)-(-2)=-8+2=-6 }\) \(\large\color{black}{ \displaystyle (-2)-(4)=-6 }\) \(\large\color{black}{ \displaystyle (4)-(10)=-6 }\)

  2. SolomonZelman
    • one year ago
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    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)

  3. SolomonZelman
    • one year ago
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    So you have a slope of -6, and (lets choose) a point (0, -8)

  4. SolomonZelman
    • one year ago
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    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...

  5. anonymous
    • one year ago
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    so it would be 6x-8, then?

  6. anonymous
    • one year ago
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    wait let me check

  7. SolomonZelman
    • one year ago
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    yes, that is correct:)

  8. anonymous
    • one year ago
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    yay! you are so helpful. :)

  9. SolomonZelman
    • one year ago
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    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.

  10. SolomonZelman
    • one year ago
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    yw

  11. anonymous
    • one year ago
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    You are awesome. :))

  12. SolomonZelman
    • one year ago
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    Thank you!

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