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1 Attachment
average rate of change = change in y / change in x
you're going from x=3 to x=5 so, chang ein x = 5-3 = 2

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do u knw how to find change in y, from the given table ?
But what about the 1 ?
And no , all of this is confusing to me :(
its okay to get confuse when u start... did u get how we got the change in x ?
Yes, we subtracted them? :o
yes, now look at table. and tell me wats the y value, when x = 5 and when x = 3
When x=5 , the y value is -2 . When x=3 , the y value is 4
excellent ! so change in y = -2-4 = -6
average rate of change = change in y / change in x = -6/2 = -3
see if that makes sense
That does makes sense ! :D
cool :)
Thank you so much, I have a few more questions? Would you be willing to help?
sure ask :)
I will attach it as a picture so it will be easier :)
1 Attachment
find m, the rate of change of first
(-1, 3) and (1 , 7)
those are the given points
(-1, 3) and (1 , 7) x1 y1 x2 y2
rate of change , m = change in y / change in x = y2-y1 / x2-x1
= 7-3 / 1--1 = 4/2 =2 so, m = 2
Right :) I'm working it out on paper with you :P
now, use this :- equation of line in slope, point form is, y - y1 = m(x-x1) plugin values :)
That would be y - 3 = 2 (x - (-1)) ?
Yes !
Yay !!
So is that it ? :o
not yet, thats one equation. we could have used the second point aswell... let me do it for you :)
Oh , okay :) Thank you !
slope m = 2, second point (1 , 7) so m = 2, x1 = 1, y1=7 y-y1 = m(x-x1) plugin values now
y-7 = 2(x-1)
thats the second equation. now see which one exists in the given options , and tick that one...
It's option 2 ! :)
You helped me understand this ! Thank you :D
Yes ! takes time to master these... i see you're already getting good at these :)
I have 3 more questions left and 2 are easy , once I answer those may you help me with the very last question ?? Pleasee :p
np, i hav time :)
just holler when u r done wid the two prblms... ;)
Haha okay !! :)
Okay here's the last question :) Jack and Jill had 3 pails of water. Each trip up the hill, Jack and Jill obtained 1 more bucket of water. Which of the graphs below represents Jack and Jill's number of pails over time?
check ur 3rd & 4th graphs. they are same !
That's how it is on my quiz :( It's probably an error ... Is there anyway to do this and figure out the answer and see if it's on one of the graphs ? If not , I don't think my teacher will deduct points for the question being incorrect lol
ohk, but wat wud u pick whe u have two exact same graphs ?
Ugh I'm just going to chose an answer and tell my teacher there was an error with the questions . Thank you though :)
good :) here is how we solve it :- since to start with, they have 3 pails of water, that means, the line must cit the y- axis at 3
since the line is cutting y-axis at 3 only in 3rd & 4th graphs, one of them must be ur answer
and since, both graphs are exact same, u toss a coin and pick one
Haha okay :) Thank you so much for your help :)
np :) goodluck wid ur assignment :)
WAITTT ! This one ?? :o
Can you help ? :o
ha, take first equation, and solve x
first equaiton :- 2x+4 = 3x-11
can you solve x ?
Yes, give me a minute :)
take ur time =)
The answer is 3 :)
Second one is 16
I need help solving the last one ...
second one is 16 \(\checkmark \)
but first one is not 3
It's not ? :( What's the first one ?
2x+4 = 3x-11 subtract 2x both sides 4 = x - 11 add 11 both sides 15 = x
first one is 15
Ohhhhh ! I know what I did wrong ! I added 3x and 2x by mistake ! haha
:) i thought so... third equation :- \(\large \frac{2x+1}{3} = \frac{x+6}{2}\)
cross multiply
How would I start ? :( I'm no good in cross multiplying ..
\(\large \frac{2x+1}{3} = \frac{x+6}{2}\) \(\large 2(2x+1) = 3(x+6)\)
Omg that makes sense -.- ! Okay I understand now !
cool :) solve x
\(\large \frac{2x+1}{3} = \frac{x+6}{2}\) \(\large 2(2x+1) = 3(x+6)\) \(\large 4x+2 = 3x+18\) solve x
4x + 2 = 3x + 18 ? Then solve ?
yes !
Okay one moment !
oki
Is x = -16 ?
\(\large \frac{2x+1}{3} = \frac{x+6}{2}\) \(\large 2(2x+1) = 3(x+6)\) \(\large 4x+2 = 3x+18\) subtract 3x both sides \(\large x+2 = 18\)
that gives, x = ?
Oh sorry I subtracted 4x by mistake !
ok.. x = ?
One sec
\(\large \frac{2x+1}{3} = \frac{x+6}{2}\) \(\large 2(2x+1) = 3(x+6)\) \(\large 4x+2 = 3x+18\) subtract 3x both sides \(\large x+2 = 18\) subtract 2 both sides \(\large x = 16\)
Should be 16 !
x = 16 ! :)
Yay :D
So equations 1 and 3 have the same solution !
yes ! so we got, first one, x = 15 second one, x = 16 third one, x = 16
careful madam, equations 2 and 3 have the same solution
THANK YOU THANK YOU THANK YOU !! :) & yes I got confused haha but now i get it :)
glad to hear that :) you're wlcme !!
Are you willing to help me out with 4 more questions ? And that it for the day !! Haha

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