Question

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

Answer 1

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

Answer 2

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)

Answer 3

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

Answer 4

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...

Answer 5

so it would be 6x-8, then?

Answer 6

wait let me check

Answer 7

yes, that is correct:)

Answer 8

yay! you are so helpful. :)

Answer 9

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.

Answer 10

yw

Answer 11

You are awesome. :))

Answer 12

Thank you!