Welcome to the presentation

on graphing lines. Let’s get started. So let’s say I had the

equation– let me make sure that this line doesn’t

show up too thick. Let’s say I had the equation–

why isn’t that showing up? Let’s see. Oh, there you go. y is equal to 2x plus 1. So this is giving a

relationship between x and y. So say x equals 1, then y would

be 2 times 1 plus 1 or 3. So for every x that we can

think of we can think of a corresponding y. So let’s do that. If we said that– put

a little table here. x and y. And let’s just throw out

some random numbers for x. If x was let’s say, negative

1, then y would be 2 times negative 1, which

is negative 2. Plus 1, which would

be negative 1. If x was 0 that’s easy. It’d be 2 times 0, which is 0. Plus 1, which is 1. If x was 1, y would be

2 times 1, which is 2. Plus 1, which is 3. If x was 2, then I think

you get the idea here. y would be 5. And we could keep on going. Obviously, there are an

infinite number of x’s we could choose and we could

pick a corresponding y. So now you see we have a

little table that gives the relationships between x and y. What we can do now is actually

graph those points on a coordinate axis. So let me see if I can draw

this somewhat neatly. I’ll use this line so

I get straight lines. That’s pretty good. Again, let me draw some

coordinate points. So let’s say that’s 1,

that’s 2, that’s 3. This is negative 1,

negative 2, negative 3. So this is the x-axis. We have 1, 2, 3. Notice we could keep going. 1, 2, 3, and this

is the y-axis. And this would be 1,

2, 3, and so on. This would be negative 1. I think you get the idea. So we can graph each

of these points. So if we have the point x is

negative 1, y is negative 1. So x, we go along the x-axis

here, and we go to x is equal to negative 1. Then we go to y is equal to

negative 1, so the point would be right here. Hope that makes sense to you. That’s the point. I’ll label it: negative

1 comma negative 1. It’s a little messy. That says negative 1

comma negative 1. That point I just

x’ed right there. Let’s do another one. That’s this point. I’ll do it in a different

color this time. Let’s say we had the

point 0 comma 1. Well, x is 0, which is here. And y is 1, so that

point is right there. Let’s do one more. If we have the point 1 comma 3. Well, 1 comma 3, x is

1 and we have y is 3. So we have the

point right there. Hope that’s making

sense for you. And we could keep graphing

them, but I think you see here, and especially if I had drawn

this a little bit neater, that these points are

forming a line. Let me draw that line in. The line looks

something like this. That’s not a good line. Let me do it better than that. The line looks

something like this. You see that? Well, that’s actually a pretty

bad line that I just drew. So it would be a line that goes

through– let me change tools. It’d be a line that goes

through here, through here, and through here. I don’t know if I’m making

this clear at all. Let me make these

points a little bit. You see the line will go

through all of these points, but it will also go through the

point 2 comma 5, which will be up here some place. For any x that you can think

of, if you had x is equal to 10,380,000,000 the

corresponding y will also be on this line. So this pink line, and it

keeps going on forever, that represents every possible

combination of x’s and y’s that will satisfy this equation. And of course, x doesn’t

have to just be whole numbers or integers. x could be pi– 3.14159. In which case it would be

someplace here and in which case y would be 2 pi plus 1. So every number that x could

be there’s a corresponding y. Let’s do another 1. So if I had the equation y is

equal to– that’s an ugly y. y is equal to negative 3x plus 5. Well, I’m going to draw it

quick and dirty this time. So that’s the x-axis. That’s the y-axis. Let’s put some values here. x and y. Let’s say if x is negative

1, then negative 1 times negative 3 is 3 plus y is 8. If x is 0, then y is 5. That’s pretty easy. If x is 1, negative 3

times 1 is negative 3. Then y is 2. If x is 2, negative 3

times 2 is negative 6. Then y is 1. Is that right? Negative 6– no, no. Negative 1. I knew something

was wrong there. So let’s graph some

of these points. So when x is negative 1 and I’m

just kind of approximating. When x is negative

1, y is negative 8. So that point would be

someplace around here. And there’s a whole module I’m

graphing coordinates if you’re finding the graphing a

coordinate pair to be a little confusing. Oh, wait. I just made a mistake. When x is negative 1, y is 9. Not negative 8, so

ignore this right here. When x is negative

1, y is positive 8. So y being up here someplace. When x is 0, y is 5. So it’d be here someplace. When x is 1, y is 2. So it’s like here. When x is 2, y is negative 1. So as you can see– and

I’ve approximated it. If I had graphing paper or if I

had a better drawn chart you could have seen it and it would

have been exactly right. I think this line

will do the job. That every point that satisfies

this equation actually falls on this line. And something interesting

here I’ll point out. You notice that this line

it slopes downwards. It goes from the top left

to the bottom right. While the line we had drawn

before had gone from the bottom left to the top right. Is there anything about this

equation that seems a little bit different than the last? I’ll give you a little

bit of a hint. This number– the negative 3,

or you could say that the coefficient on x– that

determines whether the line slopes upward, or the line

slows downward, and it tells you also how steep the line is. And that actually,

negative 3 is the slope. And I’m going to do a whole

nother module on slope. And this number here is

called the y-intercept. And that actually tells

you where you’re going to intersect the y-axis. And it turns out here,

that you intersect the axis at 0 comma 5. Let’s do one more real fast. y is equal to 2–

we already did 2x. y is equal to 1/2 x

plus 2 So real fast. x and y. And you only need two

points for a line, really. So you could just say

let’s say, x equals 0. That’s easy. y equals 2. And if x equals 2

then y equals 3. So before when we were doing 3

and 4 points that was just to kind of show you, but you

really just need two points for a line. So 0 comma 1 2. So that’s on there. And then 1, 2 comma 3. So it’s there. So the line is going to

look something like this. So notice here, once again,

we’re upward sloping and that’s because this 1/2 is positive. But we’re not sloping– we’re

not moving up as quickly as when we had y equals

2x. y equals 2x looked something like this. It was sloping up much,

much, much faster. I hope I’m not confusing you. And then the y intercept of

course is at 0 comma 2, which is right here. So if you ever want to graph

a line it’s really easy. You have to just try out some

points and you can graph it. And now in the next module I’m

going to show you a little bit more about slope and

y-intercept and you won’t even have to do this. But this gives you good

intuitive feel, I think, what a graph of a line is. I hope you have fun.

And you don't deserve one either. Mr. Khan taught me well enough that I stopped using a calculator.

So boring that you can't spell?

I didn't ask for one, nor do people think I deserve one, nor do I think that I deserve one. The Nobel Peace Prize is for PEACE, not teaching.

I did not understand how you got 3 on the last equation that you did (x,y graph) y= 1/2 + 2. you said if x=0 then y=2, which makes sense, but then you go to say x=2 then y=3 and I don't understand how you got y?

Thanks a lot for this video

What program do you use for this?

Thanks for the video I finally remember how to do this..

Thx for the vid

Helped me and I'm sure everyone else a bunch

Peace

how do u get dislikes???

thank you for helping because it helped me very much. I was struggling a lot. I'm in 7th grade and my teacher was teaching me this but I didn't get it. When i saw this video I tried the problems and I finally got it.

thanksalot this is the easiest way

of learning anything:)

Thumbs up if you have a math test tomorrow

Ladie Hensley, it's 1/2*x so 1/2*2 which is one and 1 plus 2 is three.

Great video, makes linear equations easy to understand.

Love u Khan u saved my but

Don't blame ya teachers suck khan is better than a week long lesson!!!

Thx a lot this really helped a lot

My teacher made this seem like rocket science.

you're daughter is not smart

Your*

i'm what awesome yep smart yep

I'm an aspiring teacher. I'm going to try some of these strategies in my lectures.

"Hope you have fun" No;-;

thankyou, my teacher just sucks at teaching, she expects us to all know everything and doesn't explain properly, now I can stop stressing and just watch your videos and learn math here, thankyou!

Thanks my man and remain blessed by the Most High.

thank you s much. you people r God sends

Khan Academy, if it weren't for you I wouldn't have made it through most of my math, thank you

ms paint :')

thx for the help

Hey guys do u knw that salman khan is a bangladeshi

Thank you!!! I have a huge math test tomorrow and khan academy really helps when I need it.

Thanks for the help. You ROCK!

OMG! I get it now. THANKS!!!!!!!!!!!!!!!

This is so confusing

Gunna ace this Math Exam thanks to you!!!

I understand everything except the the beginning where you have to insert the values for x… Do you pick random number how do you pick your values for x? +Khan Academy

it didn't help me at all

i dont get when its like, one over two plus 3, for example what does that even mean?

What if you have equations like Y=3? or Y=-2?

You know this video is 5 years old and he might not respond to you guys

Holy crap. algebra is the bane of my existence

To whoever's reading this: RIP

We're all in this together

why does my third ordered pair is way off but my first 2 connect perfectly?

2006! whaat

Thank you for the great video.

OH MY GOD I DID IT

what if its y equals to -5 ??

Its a little old. Fucking update it!!!

thanks I have an eoi tomorrow and this review was very helpful

Thank you 😜

My stupid math textbook didn't explain this but you did in this video.

Thank god you saved me again 🙂

We're all in this together

When you have your Algebra 1 EOC tomorrow 😅

great video

i love this dude thanks a lot wish he was my actual teacher for math lol

"Lets draw it quick n' dirty here." lolololololol

👍👍👍👍👍👍👍

You've actually got me interested in math for the first time in my life. That, alone, is an incredible achievement.

he should add his cousin more XD

anyone?

urmm…

hello?

Is Sal stoned?

hhhhhhhhmmmmmmmmmmmmm😕😕😕😕😕😕😕😕😮😮😮😮

U giys werd

IM dArpY :::::::::::::::::::::::::::::::::::::::::::::::::::::::::

THANK YOU SOO MUCH😇

came here to find help on my question whic is F(x)=-2x and i had to graph it but this shit never helped

Guys just remember when you want to find the x-intercept without having to draw a table just make y=0 eg. y = 2x + 4

0 = 2x + 4

-4 = 2x

-4/2 = 2x/2

-2 = x-intercept

The x-intercept is the same as the y-intercept as the function of showing you where the line crosses on the x-axis.

Hope this helped!

took me several weeks ti figure out…. yiu guys actually mean…

Y EQUALS Z….. THE END.

ALL OTHER MAYHMATIC DETAILS ARE NOT AS IMPORTANT…. YESYESYES… Z TIMES 1 + 1 IS ALL GOOD N WELL. …

TO THE STUDENTS STRUGGLEING LIKE ME… I HOPE 1PERSON GETS MY POINT…. GETS HELP.

SAL! LUV UR VIDS BRO.

BUTTTTTTT…. A TINY BIT IF EMPHASIZE ON THE GD RELAVANTPOINT IF Y IS Z… SYRE2 WOULDA HELPED ME… BRA! :-*

I meant type 2 not Z… I dont have time to correct every stupid message. text. comment… unless its way wrong…. hence… y equals 2 times x plus 1…I just needed THAT MORE CLEARLY EXPLAINED… BUT IN HIGH MATH- KNOWING HOW TO DESCRIBE YOUR AREAS OF MISSUNDERSTANDINGS ALONE! IS WAY TUFF….

TEACHER I.M HAVN TROUBLE…. with what? ECEDYTHING U ASS! (so we don't ask for help. how idiots? ) omfg algebra is tuff…. 🙁

Thanks! This video helped me a lot!

I'm in 6th grade Math act our teacher making us do this

nice ok not bad

put the y in the middle of the equation please

thanks alot this helped i have to do this for form 2 math grade 7 for Americans

Thanks this video really helped

hope this is making sense for you….. -_-

This really does not help at all. All those made up numbers did not tell me how to solve the equation, and I still do not know how to find the slope and what m= is.

Yo does everyone that teaches this have to be a weirdo 🤦🏾♂️

this dude draws like aids.

thanks a lot!

<3

Welp I'm taking a pre-calculus graphing class next semester, wish me luck ppl –

_________–I'm screwed….. I don't get the beginning but the rest I do

that was easy, why do I remember this being so hard in school

Khan Academy, thank you. I'm trying to catch up with my algebra (knowledge and understanding-wise) which I think I missed a year's worth of. I never really understood the concepts in class (mostly because my classmates are a bit too talkative, even when the teacher is discussing) but you explain them in a way I understand. Bless you.

Thanks so much. My math teacher leatrally sucks at teaching sooo bad especially since she has an indian accent

I understand everything except the the beginning where you have to insert the values for x… Do you pick random number how do you pick your values for x? +Khan Academy

good video

m,m

Tysm. My teacher teaches really bad, so i didnt understand this. I didnt know how to do my homework (and neither my classmates). I watched this and understood everything.

You did a great job. Take it easy on yourself!Everyone should appreciate free open access to education.

Oml duddeeee thanks 🙏🙏🙏

whos watching n 2019

One of the first vids on this channel

Grade 9 math sucks.

Right now you are saving a sister from a bad grade thank you so much!!

Whoop whoop got a test tomorrowwwww