Introduction to the coordinate plane | Introduction to algebra | Algebra I | Khan Academy

Bridging algebra and geometry. What makes linear equations so linear.

Missed the previous lesson?

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

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[naj]

so this is the dude that caused it all

[dalsenov]

This was one of greatest Descartes's genius stroke!
What Descartes did is similar to the saying:
" A picture is worth a thousand words".
For Descartes, "A picture is worth a thousand numbers, or an infinity".
The graph of a function is a picture that describes the whole function.
Visualization helps a lot.   

[eveemurcia]

My whole life...it cannot be this easy? All hail the man with this glorious voice!

[Summonspaceqex]

If school would look like this, crime rates would be lower

[oSoloDolo]

This is how math needs to be taught. Keep it up, Sal.

[ichimori]

I love how you give introduction that our shallow mind can cope with then on with the deeper stuff. The first page of my textbook literally said, " *Chapter 6: Geometry Coordinates. Calculating distance between two points.* " umm what.

[arunkumaralagarsamy]

My mind 🤯 after I saw this connection between algebra and geometry. OMG! You are such a wonderful teacher 😍

[kellysanborn]

Relationship is like math have you looked at x and wonder y

[noellundstrom]

watching this in complex analysis clears my mind and reminds me how far Ive come and to keep going :^)

[phazon]

All these European/European descended scientists and mathematicians are truly amazing. I'm one of them.

[SkiptotheLou]

I really appreciate these videos. I am not a Math person, but understanding where these concepts come from and WHY they exist makes math so much easier. Learning math in a vacuum and by the route memorization of rules is THE WORST WAY EVER.

[khalidovic]

Thank You Sal, You're definetly a LEGEND.

[albertuskundratis]

Didn't Rene Descarte suddenly arrive at his revolutionary idea that led to analytic geometry by observing this Fly enter the room, going from one wall to another? The Fly (like the gadfly of Socrates in Plato's Republic, kept intruding on his quiet meditating: "I Think, Therefore I Am or "Cogito ergo sum!" to The Fly IS, therefore x, y, &z, as vector components also ARE, and Therefore, Analytic Geometry also IS!)) suggested to Rene that the fly could be replaced by a variable letter x, y, or z! as it flew from one wall to the next or as it flew to land on a window, or landed on the floor, etc, x, y, & z could locate anywhere on the x, y, or z axis (suggested to Rene by the walls of the bedroom intersecting at the origin (0, 0, 0) at a corner of the bedroom where every wall and the floor and ceiling converged into one origin...This was not The Curse of the Fly but the Fly's Blessing!

[FollowerofDuck]

i love how he explains exactly how and why the concepts are connected

[raki-yi]

this is a great video, I always wanted to know these great mathematicians thought processes on these discoveries, this makes math more fun and intuitive.

[Unl]

If I had been taught maths this way when I was younger, I would have respected and loved maths and not have been daunted with it. "How come that works? Prove it! I don't understand why it works!" I was the kid who wanted proof for the things he was taught, and wanted to understand the reasoning behind these ideas rather than just be told "it just is". If maths had been taught that way, the students who hate maths would realize that it does indeed make sense and that it is very important.

[valeriestanglova]

Thank you, you saved me from failing this half-year.

[dolphfps]

That quote, "You just keep pushing. You just keep pushing. I made every mistake that could be made. But I kept pushing." Does NOT seem un-famous, but it is still his least famous quote. THIS IS INCREDIBLE

[ProducShuns]

On a not completely related point, this kind of math used to be my favourite in high school. This and differentiation/integration.

[CaryDominic]

I really love the way you teach Math in your videos