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LaynaMae
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ganeshie8
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average rate of change = change in y / change in x
ganeshie8
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you're going from x=3 to x=5
so, chang ein x = 5-3 = 2
ganeshie8
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do u knw how to find change in y, from the given table ?
LaynaMae
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But what about the 1 ?
LaynaMae
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And no , all of this is confusing to me :(
ganeshie8
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its okay to get confuse when u start... did u get how we got the change in x ?
LaynaMae
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Yes, we subtracted them? :o
ganeshie8
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yes, now look at table.
and tell me wats the y value, when x = 5
and when x = 3
LaynaMae
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When x=5 , the y value is -2 . When x=3 , the y value is 4
ganeshie8
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excellent !
so change in y = -2-4 = -6
ganeshie8
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average rate of change = change in y / change in x
= -6/2
= -3
ganeshie8
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see if that makes sense
LaynaMae
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That does makes sense ! :D
ganeshie8
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cool :)
LaynaMae
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Thank you so much, I have a few more questions? Would you be willing to help?
ganeshie8
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sure ask :)
LaynaMae
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I will attach it as a picture so it will be easier :)
ganeshie8
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find m, the rate of change of first
ganeshie8
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(-1, 3) and (1 , 7)
ganeshie8
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those are the given points
ganeshie8
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(-1, 3) and (1 , 7)
x1 y1 x2 y2
ganeshie8
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rate of change , m = change in y / change in x
= y2-y1 / x2-x1
ganeshie8
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= 7-3 / 1--1
= 4/2
=2
so, m = 2
LaynaMae
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Right :) I'm working it out on paper with you :P
ganeshie8
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now, use this :-
equation of line in slope, point form is,
y - y1 = m(x-x1)
plugin values :)
LaynaMae
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That would be y - 3 = 2 (x - (-1)) ?
ganeshie8
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Yes !
LaynaMae
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Yay !!
LaynaMae
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So is that it ? :o
ganeshie8
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not yet, thats one equation. we could have used the second point aswell... let me do it for you :)
LaynaMae
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Oh , okay :) Thank you !
ganeshie8
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slope m = 2, second point (1 , 7)
so m = 2, x1 = 1, y1=7
y-y1 = m(x-x1)
plugin values now
ganeshie8
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y-7 = 2(x-1)
ganeshie8
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thats the second equation.
now see which one exists in the given options , and tick that one...
LaynaMae
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It's option 2 ! :)
LaynaMae
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You helped me understand this ! Thank you :D
ganeshie8
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Yes ! takes time to master these... i see you're already getting good at these :)
LaynaMae
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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
ganeshie8
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np, i hav time :)
ganeshie8
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just holler when u r done wid the two prblms... ;)
LaynaMae
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Haha okay !! :)
LaynaMae
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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?
ganeshie8
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check ur 3rd & 4th graphs. they are same !
LaynaMae
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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
ganeshie8
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ohk, but wat wud u pick whe u have two exact same graphs ?
LaynaMae
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Ugh I'm just going to chose an answer and tell my teacher there was an error with the questions . Thank you though :)
ganeshie8
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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
ganeshie8
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since the line is cutting y-axis at 3 only in 3rd & 4th graphs, one of them must be ur answer
ganeshie8
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and since, both graphs are exact same, u toss a coin and pick one
LaynaMae
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Haha okay :) Thank you so much for your help :)
ganeshie8
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np :) goodluck wid ur assignment :)
LaynaMae
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WAITTT ! This one ?? :o
LaynaMae
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Can you help ? :o
ganeshie8
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ha, take first equation, and solve x
ganeshie8
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first equaiton :-
2x+4 = 3x-11
ganeshie8
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can you solve x ?
LaynaMae
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Yes, give me a minute :)
ganeshie8
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take ur time =)
LaynaMae
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The answer is 3 :)
LaynaMae
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Second one is 16
LaynaMae
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I need help solving the last one ...
ganeshie8
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second one is 16 \(\checkmark \)
ganeshie8
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but first one is not 3
LaynaMae
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It's not ? :( What's the first one ?
ganeshie8
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2x+4 = 3x-11
subtract 2x both sides
4 = x - 11
add 11 both sides
15 = x
ganeshie8
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first one is 15
LaynaMae
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Ohhhhh ! I know what I did wrong ! I added 3x and 2x by mistake ! haha
ganeshie8
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:) i thought so...
third equation :-
\(\large \frac{2x+1}{3} = \frac{x+6}{2}\)
ganeshie8
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cross multiply
LaynaMae
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How would I start ? :( I'm no good in cross multiplying ..
ganeshie8
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\(\large \frac{2x+1}{3} = \frac{x+6}{2}\)
\(\large 2(2x+1) = 3(x+6)\)
LaynaMae
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Omg that makes sense -.- ! Okay I understand now !
ganeshie8
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cool :) solve x
ganeshie8
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\(\large \frac{2x+1}{3} = \frac{x+6}{2}\)
\(\large 2(2x+1) = 3(x+6)\)
\(\large 4x+2 = 3x+18\)
solve x
LaynaMae
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4x + 2 = 3x + 18 ? Then solve ?
ganeshie8
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yes !
LaynaMae
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Okay one moment !
ganeshie8
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oki
LaynaMae
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Is x = -16 ?
ganeshie8
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\(\large \frac{2x+1}{3} = \frac{x+6}{2}\)
\(\large 2(2x+1) = 3(x+6)\)
\(\large 4x+2 = 3x+18\)
subtract 3x both sides
\(\large x+2 = 18\)
ganeshie8
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that gives, x = ?
LaynaMae
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Oh sorry I subtracted 4x by mistake !
ganeshie8
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ok.. x = ?
LaynaMae
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One sec
ganeshie8
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\(\large \frac{2x+1}{3} = \frac{x+6}{2}\)
\(\large 2(2x+1) = 3(x+6)\)
\(\large 4x+2 = 3x+18\)
subtract 3x both sides
\(\large x+2 = 18\)
subtract 2 both sides
\(\large x = 16\)
LaynaMae
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Should be 16 !
ganeshie8
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x = 16 ! :)
LaynaMae
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Yay :D
LaynaMae
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So equations 1 and 3 have the same solution !
ganeshie8
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yes !
so we got,
first one, x = 15
second one, x = 16
third one, x = 16
ganeshie8
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careful madam, equations 2 and 3 have the same solution
LaynaMae
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THANK YOU THANK YOU THANK YOU !! :) & yes I got confused haha but now i get it :)
ganeshie8
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glad to hear that :) you're wlcme !!
LaynaMae
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Are you willing to help me out with 4 more questions ? And that it for the day !! Haha