Someone check to see if I'm right?

- teller

Someone check to see if I'm right?

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- teller

It would be going up by 4

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- teller

@jim_thompson5910 mind helping me once again ?I know it's going up by 4 so would it be -n-4?

- jim_thompson5910

going up by 4? how did you get that?

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## More answers

- teller

-8 to -11 is going up by four and then from -11 to -14 it's going up by four and then from -14 to -17 it's going up by four.

- jim_thompson5910

actually the change from 8 to 11 is +3
but we're going from a small negative (-8) to a larger negative (-11)
so when we do this, we subtract 3 each time

- jim_thompson5910

draw out a number line to check
plot -8 and move 3 units to the left to get to -11
moving 3 units to the left means "subtract 3"

- teller

so it would be a negative 3 ? so -n-3? or no |dw:1441678898311:dw|

- jim_thompson5910

let's check that

- jim_thompson5910

if `-n-3` was the function rule, then it should take n = 1 and it should produce -8 as the output
but if n = 1, then
-n-3 = -1-3 = -4
which is NOT equal to -8 like we want

- teller

So what do we do?

- jim_thompson5910

let's first find the slope

- jim_thompson5910

what's the change in x?
the change in y?

- teller

3?

- teller

well for the input 1 and for the output 3

- jim_thompson5910

as x increases by 1, y decreases by 3
change in x = 1
change in y = -3
agreed?

- teller

Yes

- jim_thompson5910

what would be the slope?

- teller

um I don't know not good with slopes.. would it be n+1=-3?

- jim_thompson5910

hopefully you wrote down the slope formula I posted on your last question

- jim_thompson5910

I would write that in your notes

- teller

I don't have it on me mind rewriting it?

- jim_thompson5910

ok write it down in your notes or somewhere where you can remember
\[\Large \text{Slope} = \frac{\text{Change in y}}{\text{Change in x}}\]

- teller

so slope= 1 over -3?

- jim_thompson5910

you'll also see this slope formula as well (write this in your notes too)
\[\Large \text{Slope} = m = \frac{y_2-y_1}{x_2-x_1}\]
m is often used as the slope

- jim_thompson5910

you have it backwards
it should be -3 over 1

- teller

but i thought 1 was y?

- jim_thompson5910

|dw:1441679829877:dw|

- jim_thompson5910

|dw:1441679911895:dw|

- teller

Okay so slope = -3 over 1

- jim_thompson5910

|dw:1441679926075:dw|

- jim_thompson5910

so that's why
change in x = 1
change in y = -3

- teller

so would it be n+1-3?

- jim_thompson5910

so you see why the slope is -3?

- teller

Yea I guess but is my answer correct or no?

- jim_thompson5910

no it's not correct

- jim_thompson5910

let's say hypothetically that x increased by 2 (instead of 1). The change in y stays the same. What would be the slope this time?

- teller

Um slope=-3 over 2..

- jim_thompson5910

yes, -3/2 which is equivalent to -1.5

- jim_thompson5910

anyways, back to this problem
the slope is m = -3

- jim_thompson5910

pick any input,output pair you want. Which do you choose?

- teller

idk um the original I guess 1 -8

- jim_thompson5910

sure let's go with that

- jim_thompson5910

m = -3 is the slope
x = 1 and y = -8 is the input/output pair

- jim_thompson5910

plug those three values into y = mx+b and solve for b

- teller

Just to be clear it would be written like this right ? -8=m1+b or no?

- jim_thompson5910

replace m with -3

- teller

oh okay

- teller

so how do I write the one it will just look like -31..

- jim_thompson5910

mx is the same as m*x
so m*x = -3*1 = -3

- teller

oh okay

- teller

-5?

- jim_thompson5910

yes if you solve -8=-3+b for b, you get b = -5

- jim_thompson5910

summary:
m = -3 is the slope
b = -5 is the y intercept

- jim_thompson5910

y = mx+b turns into y = -3x-5

- teller

so n x-3-5? is the final answer or no n=-3x-5?

- jim_thompson5910

recall from last time, we can replace x with n

- jim_thompson5910

so the rule -3x-5 is the same as -3n-5

- teller

so -3n-5 is the final answer ?

- jim_thompson5910

yeah, plug in n = 1 and you should get -8
plug in n = 2 and you should get -11
etc etc
I recommend you actually plug in all of the n values from n = 1 to n = 4 to check them all

- teller

Okay can you help me on another one once I try it out?

- jim_thompson5910

alright

- teller

So input goes up 1 and output goes up 2
so slope = 2/1
so if i take the first combinations 1 and 10 it would be 10=2*1+b which gives me b=8 so would it be 2n+8?

##### 1 Attachment

- teller

@jim_thompson5910

- jim_thompson5910

very good, you nailed it

- jim_thompson5910

to check your answer, you can plug in values of n
if n = 1
2n+8 = 2*1 + 8 = 2+8 = 10
so that checks out
if n = 2
2*n+8 = 2*2+8 = 12
that checks out as well
etc etc

- teller

Thank you!You've help me a lot more than what that video will ever do.

- jim_thompson5910

I'm glad I could be of help. I'm not sure why the teacher had you watch it when she uses an odd method to find the function rule. If anything, she doesn't mention how to find the generalized rule in terms of n (just how to extend out the table and find outputs for specific inputs).

- teller

Yea same I did have a question is the out put goes from a negative to a positive what happens? for example -3 ,-1,1,3 ?

- jim_thompson5910

-3 ,-1,1,3 is your list of outputs?

- teller

yes

- teller

the list of inputs are 1 2 3 4 n

- teller

I would say the output is 2 right?

- teller

or -2

- jim_thompson5910

I think you mean +2
basically you increase the outputs by 2 each time the inputs increase by 1

- jim_thompson5910

change in y = +2
change in x = +1
slope = ???

- teller

slope = 1 over 2?

- jim_thompson5910

you have it flipped again

- teller

opps slope =2 over 1

- jim_thompson5910

yeah 2/1 = 2

- teller

so -3=2*1+b?

- teller

which would give me -5

- jim_thompson5910

yep

- teller

so-5n+2

- jim_thompson5910

you mixed up m and b

- jim_thompson5910

y = mx+b

- teller

What you mean?

- teller

-5=2*1+b right?

- jim_thompson5910

you found m = 2 and b = -5
so y = mx+b turns into y = 2x-5

- teller

oh wait no it's -3 not -5 ,-5 is the answer.

- teller

-3=2*1+b

- teller

which gave me -5

- jim_thompson5910

do you see how I got y = 2x-5 ?

- teller

oh wait so it would be 2n-5

- jim_thompson5910

yeah you drop the y= part
then change x to n

- jim_thompson5910

if the input is n, then the output is 2n-5

- teller

Yea I was getting confused

- jim_thompson5910

but it's all making sense now? or no?

- teller

Input 1
output -2 ?
slope = -2 over 1
-10=-2*1+b = -12
-2n-12?

##### 1 Attachment

- jim_thompson5910

going from -10 to -13 is a change of -3

- jim_thompson5910

-13 ---> -16
change of -3

- jim_thompson5910

and so on

- teller

oh okay so -3n-7

- jim_thompson5910

correct

- teller

Alright thank you so much.That's all I have right now.

- jim_thompson5910

glad that it's making sense

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