## 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

1. 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. $$\large\color{black}{ \displaystyle (-8)-(-2)=-8+2=-6 }$$ $$\large\color{black}{ \displaystyle (-2)-(4)=-6 }$$ $$\large\color{black}{ \displaystyle (4)-(10)=-6 }$$

2. 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)

3. SolomonZelman

So you have a slope of -6, and (lets choose) a point (0, -8)

4. 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...

5. anonymous

so it would be 6x-8, then?

6. anonymous

wait let me check

7. SolomonZelman

yes, that is correct:)

8. anonymous

yay! you are so helpful. :)

9. 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.

10. SolomonZelman

yw

11. anonymous

You are awesome. :))

12. SolomonZelman

Thank you!