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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

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 :)

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 :)

np, i hav time :)

just holler when u r done wid the two prblms... ;)

Haha okay !! :)

check ur 3rd & 4th graphs. they are same !

ohk, but wat wud u pick whe u have two exact same graphs ?

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

4x + 2 = 3x + 18 ? Then solve ?

yes !

Okay one moment !

oki

Is x = -16 ?

that gives, x = ?

Oh sorry I subtracted 4x by mistake !

ok.. x = ?

One sec

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