Algebra: graphing lines 1

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
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.

100 thoughts on “Algebra: graphing lines 1”

• March 4, 2013 at 11:18 am

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

• March 4, 2013 at 11:19 am

So boring that you can't spell?

• March 4, 2013 at 4:05 pm

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.

• March 9, 2013 at 7:30 pm

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?

• March 16, 2013 at 8:21 am

Thanks a lot for this video

• April 7, 2013 at 2:11 pm

What program do you use for this?

• April 14, 2013 at 8:50 pm

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

• April 21, 2013 at 6:21 pm

Thx for the vid
Helped me and I'm sure everyone else a bunch
Peace

• April 22, 2013 at 8:49 am

how do u get dislikes???

• May 1, 2013 at 2:47 am

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.

• June 7, 2013 at 10:13 am

thanksalot this is the easiest way
of learning anything:)

• June 9, 2013 at 5:17 pm

Thumbs up if you have a math test tomorrow

• August 4, 2013 at 5:28 pm

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

• August 9, 2013 at 10:25 pm

Great video, makes linear equations easy to understand.

• August 10, 2013 at 1:26 am

Love u Khan u saved my but

• August 14, 2013 at 4:19 am

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

• September 13, 2013 at 10:38 pm

Thx a lot this really helped a lot

• September 24, 2013 at 7:42 pm

My teacher made this seem like rocket science.

• October 23, 2013 at 9:02 pm

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• October 25, 2013 at 9:14 pm

Your*

• October 29, 2013 at 1:11 am

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• November 23, 2013 at 6:29 am

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

• February 8, 2014 at 7:45 pm

"Hope you have fun" No;-;

• February 11, 2014 at 1:04 am

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!

• February 16, 2014 at 2:24 pm

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• February 23, 2014 at 3:07 pm

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• April 6, 2014 at 11:06 pm

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

• April 29, 2014 at 8:40 pm

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• December 13, 2014 at 5:33 pm

thx for the help

• January 18, 2015 at 4:13 pm

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• February 12, 2015 at 3:47 am

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

• February 23, 2015 at 2:15 am

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• May 21, 2015 at 6:38 pm

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

• June 4, 2015 at 3:48 pm

This is so confusing

• June 22, 2015 at 9:21 pm

Gunna ace this Math Exam thanks to you!!!

• September 4, 2015 at 7:10 pm

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

• October 21, 2015 at 3:39 am

it didn't help me at all

• November 17, 2015 at 12:45 am

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

• December 8, 2015 at 4:31 am

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

• December 10, 2015 at 9:58 pm

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

• January 5, 2016 at 4:06 pm

Holy crap. algebra is the bane of my existence

• January 30, 2016 at 1:28 pm

We're all in this together

• February 4, 2016 at 11:29 pm

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

• March 14, 2016 at 9:34 pm

2006! whaat

• March 28, 2016 at 3:25 pm

Thank you for the great video.

• March 30, 2016 at 4:37 am

OH MY GOD I DID IT

• April 6, 2016 at 7:41 am

what if its y equals to -5 ??

• April 10, 2016 at 3:26 pm

Its a little old. Fucking update it!!!

• April 13, 2016 at 1:09 am

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

• April 13, 2016 at 3:24 pm

Thank you 😜

• April 13, 2016 at 3:28 pm

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

• April 26, 2016 at 3:53 am

Thank god you saved me again 🙂

• April 27, 2016 at 4:00 pm

We're all in this together

• May 3, 2016 at 1:06 am

When you have your Algebra 1 EOC tomorrow 😅

• June 17, 2016 at 7:15 am

great video

• June 28, 2016 at 2:50 am

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

• June 30, 2016 at 2:43 am

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

• July 8, 2016 at 7:32 pm

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• August 19, 2016 at 1:38 am

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

• August 31, 2016 at 10:29 am

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• September 19, 2016 at 2:09 pm

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• September 26, 2016 at 11:00 pm

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• October 27, 2016 at 9:59 pm

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• October 27, 2016 at 9:59 pm

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

• October 30, 2016 at 5:59 pm

THANK YOU SOO MUCH😇

• November 2, 2016 at 9:08 pm

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

• November 15, 2016 at 12:01 pm

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!

• November 24, 2016 at 9:43 am

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! :-*

• November 24, 2016 at 9:54 am

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…. 🙁

• November 29, 2016 at 6:15 am

Thanks! This video helped me a lot!

• December 29, 2016 at 9:25 am

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

• January 21, 2017 at 12:45 pm

• January 21, 2017 at 6:11 pm

put the y in the middle of the equation please

• February 3, 2017 at 11:26 pm

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

• February 5, 2017 at 8:00 pm

Thanks this video really helped

• March 8, 2017 at 8:27 pm

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

• March 23, 2017 at 5:50 pm

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.

• March 27, 2017 at 3:40 am

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

• April 19, 2017 at 8:14 pm

this dude draws like aids.

• May 16, 2017 at 12:28 am

thanks a lot!

• June 4, 2017 at 2:37 pm

<3

• July 26, 2017 at 10:35 am

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

• September 6, 2017 at 3:16 am

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

• September 21, 2017 at 6:16 am

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

• November 12, 2017 at 4:24 am

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.

• January 26, 2018 at 1:22 am

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

• February 24, 2018 at 8:09 am

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

• March 26, 2018 at 8:55 am

good video

• August 15, 2018 at 2:22 pm

m,m

• September 25, 2018 at 6:37 pm

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.

• October 18, 2018 at 11:37 pm

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

• October 30, 2018 at 11:47 pm

Oml duddeeee thanks 🙏🙏🙏

• January 31, 2019 at 2:03 am

whos watching n 2019

• February 25, 2019 at 1:18 am

One of the first vids on this channel

• March 4, 2019 at 4:37 am