teller
  • teller
Someone check to see if I'm right?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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teller
  • teller
It would be going up by 4
teller
  • teller
@jim_thompson5910 mind helping me once again ?I know it's going up by 4 so would it be -n-4?
jim_thompson5910
  • jim_thompson5910
going up by 4? how did you get that?

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teller
  • 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
  • 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
  • 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
  • teller
so it would be a negative 3 ? so -n-3? or no |dw:1441678898311:dw|
jim_thompson5910
  • jim_thompson5910
let's check that
jim_thompson5910
  • 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
  • teller
So what do we do?
jim_thompson5910
  • jim_thompson5910
let's first find the slope
jim_thompson5910
  • jim_thompson5910
what's the change in x? the change in y?
teller
  • teller
3?
teller
  • teller
well for the input 1 and for the output 3
jim_thompson5910
  • jim_thompson5910
as x increases by 1, y decreases by 3 change in x = 1 change in y = -3 agreed?
teller
  • teller
Yes
jim_thompson5910
  • jim_thompson5910
what would be the slope?
teller
  • teller
um I don't know not good with slopes.. would it be n+1=-3?
jim_thompson5910
  • jim_thompson5910
hopefully you wrote down the slope formula I posted on your last question
jim_thompson5910
  • jim_thompson5910
I would write that in your notes
teller
  • teller
I don't have it on me mind rewriting it?
jim_thompson5910
  • 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
  • teller
so slope= 1 over -3?
jim_thompson5910
  • 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
  • jim_thompson5910
you have it backwards it should be -3 over 1
teller
  • teller
but i thought 1 was y?
jim_thompson5910
  • jim_thompson5910
|dw:1441679829877:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1441679911895:dw|
teller
  • teller
Okay so slope = -3 over 1
jim_thompson5910
  • jim_thompson5910
|dw:1441679926075:dw|
jim_thompson5910
  • jim_thompson5910
so that's why change in x = 1 change in y = -3
teller
  • teller
so would it be n+1-3?
jim_thompson5910
  • jim_thompson5910
so you see why the slope is -3?
teller
  • teller
Yea I guess but is my answer correct or no?
jim_thompson5910
  • jim_thompson5910
no it's not correct
jim_thompson5910
  • 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
  • teller
Um slope=-3 over 2..
jim_thompson5910
  • jim_thompson5910
yes, -3/2 which is equivalent to -1.5
jim_thompson5910
  • jim_thompson5910
anyways, back to this problem the slope is m = -3
jim_thompson5910
  • jim_thompson5910
pick any input,output pair you want. Which do you choose?
teller
  • teller
idk um the original I guess 1 -8
jim_thompson5910
  • jim_thompson5910
sure let's go with that
jim_thompson5910
  • jim_thompson5910
m = -3 is the slope x = 1 and y = -8 is the input/output pair
jim_thompson5910
  • jim_thompson5910
plug those three values into y = mx+b and solve for b
teller
  • teller
Just to be clear it would be written like this right ? -8=m1+b or no?
jim_thompson5910
  • jim_thompson5910
replace m with -3
teller
  • teller
oh okay
teller
  • teller
so how do I write the one it will just look like -31..
jim_thompson5910
  • jim_thompson5910
mx is the same as m*x so m*x = -3*1 = -3
teller
  • teller
oh okay
teller
  • teller
-5?
jim_thompson5910
  • jim_thompson5910
yes if you solve -8=-3+b for b, you get b = -5
jim_thompson5910
  • jim_thompson5910
summary: m = -3 is the slope b = -5 is the y intercept
jim_thompson5910
  • jim_thompson5910
y = mx+b turns into y = -3x-5
teller
  • teller
so n x-3-5? is the final answer or no n=-3x-5?
jim_thompson5910
  • jim_thompson5910
recall from last time, we can replace x with n
jim_thompson5910
  • jim_thompson5910
so the rule -3x-5 is the same as -3n-5
teller
  • teller
so -3n-5 is the final answer ?
jim_thompson5910
  • 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
  • teller
Okay can you help me on another one once I try it out?
jim_thompson5910
  • jim_thompson5910
alright
teller
  • 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
  • teller
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
very good, you nailed it
jim_thompson5910
  • 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
  • teller
Thank you!You've help me a lot more than what that video will ever do.
jim_thompson5910
  • 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
  • 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
  • jim_thompson5910
-3 ,-1,1,3 is your list of outputs?
teller
  • teller
yes
teller
  • teller
the list of inputs are 1 2 3 4 n
teller
  • teller
I would say the output is 2 right?
teller
  • teller
or -2
jim_thompson5910
  • jim_thompson5910
I think you mean +2 basically you increase the outputs by 2 each time the inputs increase by 1
jim_thompson5910
  • jim_thompson5910
change in y = +2 change in x = +1 slope = ???
teller
  • teller
slope = 1 over 2?
jim_thompson5910
  • jim_thompson5910
you have it flipped again
teller
  • teller
opps slope =2 over 1
jim_thompson5910
  • jim_thompson5910
yeah 2/1 = 2
teller
  • teller
so -3=2*1+b?
teller
  • teller
which would give me -5
jim_thompson5910
  • jim_thompson5910
yep
teller
  • teller
so-5n+2
jim_thompson5910
  • jim_thompson5910
you mixed up m and b
jim_thompson5910
  • jim_thompson5910
y = mx+b
teller
  • teller
What you mean?
teller
  • teller
-5=2*1+b right?
jim_thompson5910
  • jim_thompson5910
you found m = 2 and b = -5 so y = mx+b turns into y = 2x-5
teller
  • teller
oh wait no it's -3 not -5 ,-5 is the answer.
teller
  • teller
-3=2*1+b
teller
  • teller
which gave me -5
jim_thompson5910
  • jim_thompson5910
do you see how I got y = 2x-5 ?
teller
  • teller
oh wait so it would be 2n-5
jim_thompson5910
  • jim_thompson5910
yeah you drop the y= part then change x to n
jim_thompson5910
  • jim_thompson5910
if the input is n, then the output is 2n-5
teller
  • teller
Yea I was getting confused
jim_thompson5910
  • jim_thompson5910
but it's all making sense now? or no?
teller
  • teller
Input 1 output -2 ? slope = -2 over 1 -10=-2*1+b = -12 -2n-12?
jim_thompson5910
  • jim_thompson5910
going from -10 to -13 is a change of -3
jim_thompson5910
  • jim_thompson5910
-13 ---> -16 change of -3
jim_thompson5910
  • jim_thompson5910
and so on
teller
  • teller
oh okay so -3n-7
jim_thompson5910
  • jim_thompson5910
correct
teller
  • teller
Alright thank you so much.That's all I have right now.
jim_thompson5910
  • jim_thompson5910
glad that it's making sense

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