Question

what is the function rule?

x= -2, -1,0,1,2
y= 9, 4, -1, -6, -11

Answer 1

have you tried determine if it is a line or not?

Answer 2

I don't understand what you mean?

Answer 3

Are you talking about the x, y axis?

Answer 4

what i mean by line is have you tried to determine if your function is linear or not?

Answer 5

is your slope the same through out

Answer 6

\[m=\frac{y_2-y_1}{x_2-x_1} \text{ is this the same no matter what } (x_1,y_1) \text{ and } (x_2,y_2) \\ \text{ you choose from your table }\]

Answer 7

if that is then it is a line

Answer 8

and it will have form f(x)=mx+b

Answer 9

I think it is linear because the is only a difference of 5 through, and I don't think it geometric

Answer 10

notice the x values you are given are evenly spaced
and your y values form a arithmetic sequence that is there is a common difference
so it will have a common slope amongst the points given
therefore it is a linear function

Answer 11

so find the slope
then replace m in the function rule:
f(x)=mx+b with what you find the slope to be

then use one of the points to find b

Answer 12

y=-5

Answer 13

do you mean m=-5 ?

Answer 14

anyways I think you meant m=-5
\[f(x)=mx+b \\ f(x)=-5x+b\]
so now you just need to find b
use one of the points in plug them into the function rule
f(x)=-5x+b

And remember y=f(x)

Answer 15

Well 9-5=4, and 4-5=-1 and -1-5= -6 so the function for y must be - 5

Answer 16

y=f-5

Answer 17

I think you are getting the y coordinates confused with finding the slope

clearly the y's aren't always -5 so you can't say y=-5

Answer 18

oh..okay, so what does y equal then? I thought I was on the right track..

Answer 19

do you want to try to solve for b above given any of the points?

Answer 20

so far we have y=-5x+b
I was asking you to use one of the points given to find b

Answer 21

b=9??

Answer 22

what point did you use to determine that

Answer 23

..I just used the y table...

Answer 24

(-2,9) is a point on your table
(-1,4) is a point on your table
(0,-1) is a point on your table
(1,-6) is a point on your table
(2,-11) is a point on your table
you can use any of these (x,y) points to find b
in the function rule
f(x)=-5x+b

Answer 25

(0,-1) is actually the y-intercept if you didn't feel like doing any extra work

Answer 26

Okay, I got it now, my teacher never explained that to me

Answer 27

f(x)=-5x+b
b represents the y-intercept
so b is?

Answer 28

I don't know so I am guessing it's -11

Answer 29

y=mx+b
m is the slope
b is the y-intercept
is this part familiar to you?

Answer 30

No, my teacher wasn't here today to teach us this, so I am not sure

Answer 31

I am sorry

Answer 32

ok we can just use one of the points given then
y=-5x+b
using (-2,9) to solve for b
replace x with -2
and replace y with 9
9=-5(-2)+b

can you try to solve this for b?

Answer 33

is it 1?

Answer 34

close

Answer 35

2!

Answer 36

further away

-5 times -2 is 10

Answer 37

9=10+b

Answer 38

can you solve this for b now?

Answer 39

or still too hard?

Answer 40

-1?

Answer 41

yes!

Answer 42

10+(-1) is totally 9
so b=-1

Answer 43

your function rule is f(x)=-5x-1

Answer 44

and see that matches are y-intercept (0,-1)

Answer 45

that b part does

Answer 46

okay!

Answer 47

I understand, now we just do something similar for the x axis

Answer 48

what

Answer 49

your job was to find the function rule
we did that
f(x)=-5x-1

is there something else you are suppose to do besides find function rule?

Answer 50

No thank you

Answer 51

np

Answer 52

You're very helpful!

Answer 53

thank you a million times