Direct Variation - By Anywhere Math
Transcript
00:0-1 | Welcome anywhere . Math . I'm Jeff Jacobson . And | |
00:01 | today we're gonna talk about direct variation . Let's get | |
00:05 | started . Okay before we get to an example , | |
00:25 | let's talk about direct variation for a moment . Uh | |
00:29 | Two quantities X and Y would show direct variation . | |
00:34 | If you can write them in an equation like this | |
00:36 | where Y equals K . X . If you can | |
00:39 | write an equation like that then you would say X | |
00:42 | and Y show direct variation . If not if you've | |
00:46 | got something extra like minus one or plus seven then | |
00:51 | they're not showing direct variation . Okay now this k | |
00:55 | uh this case we call the constant of proportionality proportion | |
01:04 | . Now let's see it's a long word constant of | |
01:08 | proportionality . It's also basically just the slope . Mhm | |
01:15 | . Of the line . Okay if you graph it | |
01:17 | , that's what that represents . Is just the slope | |
01:19 | of the line . Okay let's get to an example | |
01:22 | . Example one tell whether X and Y show direct | |
01:25 | variation . So we have a 22 problems . We're | |
01:28 | going to do first one , we've got a table | |
01:30 | X . And Y . We've got some X . | |
01:32 | Values , we've got some Y . Values . Uh | |
01:35 | notice there's no equation so we're not gonna do it | |
01:38 | that way to see if we can if we can | |
01:40 | write the equation with Y equals K . X . | |
01:43 | Um Instead what we're gonna do is we are going | |
01:46 | to graph them . So I'm just gonna make it | |
01:49 | quick a quick little sketch uh on my X . | |
01:55 | Axis . I just got 123 on my Y . | |
01:59 | I guess . I'm sorry I need to go negative | |
02:01 | let me redo that . Yeah So I'll do all | |
02:05 | four quadrants 123 23 And then let's go uh to | |
02:15 | 40 negative two negative four . Okay ? Uh So | |
02:21 | 1st 1st ordered pair , one negative two . So | |
02:24 | one negative two would be there , Then 2020 would | |
02:28 | be there and then three two would be there . | |
02:33 | Okay connect my points and the line looks something like | |
02:38 | that . Now one other thing for X and Y | |
02:42 | to have direct variation . If you graph it , | |
02:46 | the line has to go through the origin . Okay | |
02:50 | that's really important . You should write that down . | |
02:52 | Um It has to go through the origin . And | |
02:55 | the reason if you think about it , if the | |
02:59 | equation needs to look like that , if X . | |
03:03 | Zero . Yeah . Well what is why I have | |
03:08 | to be why has to be zero as well because | |
03:11 | zero times any number We'll Give You zero . Right | |
03:15 | ? So here yeah Notice the line does not go | |
03:22 | through my origin , it does not go through 00 | |
03:24 | . So X . And Y . Here do they | |
03:26 | show direct variation ? And the answer is no they | |
03:30 | do not . Okay let's try B . So the | |
03:33 | same thing , let's graph the points . And for | |
03:37 | this they are both positive , which is nice . | |
03:39 | So I'm just going to be the first quadrant . | |
03:41 | Uh And that'll be let's go to for 24 1st | |
03:49 | point is at the origin 00 right there . And | |
03:53 | I've got to to which is there 44 ? Which | |
03:57 | is But there draw my line doesn't have to be | |
04:03 | perfect . But again notice this time my line does | |
04:07 | go through the origin and I can see right here | |
04:10 | there's the origin right there . Anyway , so really | |
04:13 | I didn't even need to graph it . I could | |
04:14 | have noticed that . Um So yes , in this | |
04:17 | situation X and Y do show direct variation . Okay | |
04:23 | , let's try another example . Alright , example to | |
04:26 | same thing tell whether X and Y show direct variation | |
04:29 | . But we're gonna tell uh in a different way | |
04:32 | . We're not going to graph each of these equations | |
04:35 | . We're not gonna grab the line instead , we're | |
04:37 | going to look to see if we can get the | |
04:39 | equation to look like why equals K . X . | |
04:44 | To do that . We're trying to get why alone | |
04:47 | , which means we're solving for why . Okay , | |
04:51 | so maybe if you want to put a little uh | |
04:53 | star here , solve for why . That's what we're | |
05:00 | trying to do . We're trying to get why alone | |
05:03 | , right ? We're isolating why . So here we | |
05:06 | go . Hopefully you remember some a little bit of | |
05:08 | algebra uh notice I'm solving for why I'm trying to | |
05:12 | get why alone . It's not alone . We have | |
05:15 | this plus one , so I need to get rid | |
05:17 | of that plus one . And I do that by | |
05:20 | subtracting one . Anything I do to one side , | |
05:22 | I have to do the other . So subtract one | |
05:24 | year uh that becomes zero , goes away and I | |
05:28 | get Y equals two X minus one . So now | |
05:34 | uh the question , does it show direct variation , | |
05:38 | does it look like Y equals K . X . | |
05:41 | Almost . It almost does . If I didn't have | |
05:44 | that -1 there it would . But because I have | |
05:48 | this two X -1 . no X . And Y | |
05:53 | . In this situation do not show direct variation because | |
05:56 | of this minus one notice there's no minus anything here | |
06:00 | . Okay it's just K . X . Um Let's | |
06:03 | look at the next one . So one half Y | |
06:05 | equals X . Again I'm solving for why I'm trying | |
06:09 | to get why alone right now , it's being multiplied | |
06:12 | by one half . So to get rid of that | |
06:15 | one half , I could divide by a half but | |
06:18 | divided by a fraction is the same thing as multiplying | |
06:22 | by , it's reciprocal . The reciprocal of one half | |
06:25 | is to over one which is two . So to | |
06:28 | solve I'm just gonna do I've got one half Y | |
06:32 | . I'm gonna multiply by 2/1 . Anything I do | |
06:37 | to one side I have to do the other . | |
06:39 | So that's gonna be come to X two times X | |
06:43 | . And this works because right the twos will cancel | |
06:46 | each other out and I basically get one Y . | |
06:49 | Which is just why Which is great all by itself | |
06:53 | . Which is what I want equals two X . | |
06:57 | In this situation , does that look like what I | |
07:01 | wanted ? Why it was K . X . Absolutely | |
07:05 | . My concept for proportionality is 2K . is to | |
07:09 | hear um I have Y equals on the one side | |
07:13 | . There's the X . So in this situation yes | |
07:18 | X . And Y . Do show correct variation . | |
07:21 | Okay here's something to try on your own . Thank | |
07:30 | you so much for watching . And if you like | |
07:32 | this video please subscribe . |
Summarizer
DESCRIPTION:
OVERVIEW:
Direct Variation is a free educational video by Anywhere Math.
This page not only allows students and teachers view Direct Variation videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.