English language
Speed:
arrow_drop_down
normal
arrow_drop_up
vertical_align_top
emoji_objects
Full Transcript
X
- in this video we are going to work on
- constructing linear models so in order
- to construct linear mouths we got to
- have some some ground rules here set out
- we talked about slope in a past video
- but we haven't talked about the
- y-intercept so the y-intercept by
- definition it's where the graph crosses
- the y axis and that makes sense when you
- think about intercept right and it's the
- Y so it's where it crosses the y axis um
- by symbol we noted as B don't ask me
- because I don't know but other infor
- interesting things when X is zero that's
- when we have the y intercept and you'll
- see that graphically X is the starting
- point so when x is zero we have the y
- intercept so therefore the y intercept
- is the starting point of the graph ok
- now our linear models are noticed as y
- equals MX plus B where m is the slope B
- is the y-intercept and you might say
- well what's this Y in this X business
- well when you graph a line the x and y
- are coordinates that represent all the
- points on the line so they will stay in
- that equation as just x and y because
- they represent everything on the line so
- that when we write equations we will
- need the slope we will need the
- y-intercept yeah that's it ok the the
- dependent variable is y the independent
- variable is X so that means that Y
- depends on X ok so Y depends on X and
- you will see that again as we work
- through examples not just in this video
- but in future videos as well
- alright so let's get to it
- David weighs 240 pounds and sets a
- weight-loss goal of 2 pounds per week
- let X okay now not every problem is
- going to tell you but sometimes they say
- let X represents the number of weeks
- which go by find the linear model which
- represents how much David hopes to weigh
- after X weeks on the plan and so it's
- really important and whether you do it
- at the beginning or the third step it's
- not bad
- you know whatever do it whatever step
- you want but what's the independent
- what's the dependent variable well they
- tell us that X is the independent
- variable is the number of weeks that
- David is on this weight-loss plan so
- after a bunch of weeks go by Y is going
- to be his weight right if he's was in 2
- pounds a week after 10 weeks he has a
- certain weight after 12 weeks he has a
- certain weight after 80 weeks he has a
- certain way so the dependent variable is
- his weight his weight depends on how
- many weeks have gone by in this weight
- loss system all right so what is the
- unit measure of X well in this case we
- are talking about weeks and you might
- say well Becky we just answered that
- here in Part B true but it's important
- to recognize and to see as we go through
- these different examples throughout the
- course of the videos the unit measure of
- x of our independent variable almost all
- almost always deals with some aspect of
- time whether it's days hours month years
- weeks right it's just time of reference
- of time now what is the y-intercept or
- the starting point well if you recall
- from our problem David's right now
- weighs 240 pounds so that is our
- starting point our starting point is 240
- when he so 0 how many weeks have gone by
- none he hasn't started yet but now he's
- gonna start and he weighs 240 what is
- the slope the slope is the rate at which
- things are changing well for time what
- is weight how is his weight changing
- well it's gonna go down to pounds a week
- two pounds in one week that's the
- constant goal anyway if it's going down
- that means decreasing so we're gonna
- have a negative two so the slope is
- negative two
- all right weights gonna go down so when
- I go to write my linear model y equals
- slope my slope is negative two times X
- where X represents the number of weeks
- plus my y-intercept which in this case
- is 240 pounds
- and it's positive because he weighs 240
- now right so this is my linear model and
- we can use do a lot of things to figure
- out how this works right so how much
- does David hope to weigh after four
- weeks well remember that means X is 4 so
- if I have y equals negative 2x plus 240
- I can go ahead and say let's plug in
- that 4 for X so y equals negative 2
- times 4 plus 240 when I solve this
- mathematically I do multiplication first
- so negative 2 times 4 is negative 8 plus
- 240 that means David will hopes to weigh
- 232 pounds after four weeks okay
- what about 10 weeks well I take that
- same formula but I plug in 10 for X and
- again I multiply so negative 20 plus 240
- David hopes to weigh 220 pounds after 10
- weeks and I'd be a great weight loss
- system right how long will it take David
- to reach his goal weighing 180 pounds on
- this plan okay well y equals negative 2x
- plus 240 180 represents his ending
- weight and why is his ending weight so
- 180 is the goal how many weeks have to
- go by on this plan well if you solve
- this we'd do the same thing to both
- sides we need to get X by itself so if I
- subtract 240 because that's you always
- want to work farthest away from your
- variable then get closer so 240 minus
- 240 gives me zero that leaves me with
- negative 2x and 180 minus 240 on this
- side gives me negative 60 I now divide
- both sides by negative 2 and x equals 30
- so that means it will take David
- approximately 30 weeks to reach his
- weight-loss goal of 180 pounds now let's
- graph this ok well I know that it's
- going to take 30 weeks to hit 180 I just
- did that well 30 weeks is over here and
- his goals at the bottom so that is down
- here but I also know that from previous
- ten weeks gives me 220 so here's 10
- I go up from 10 all over 2 to 20 so this
- is going to be not straight at all
- because I'm drawing with my finger on an
- iPad but you get a couple dots and you
- can connect them and it will be roughly
- a straight line and this is the graphic
- of David's weight-loss plan week by week
- if if everything works right it's
- actually not a horrible line I'm kind of
- impressed with myself there all right
- now if David were to raise his
- weight-loss school to 3 pounds a week
- how would the model and the graph change
- well remember his weight loss plan of
- how much per week that's the slope so
- the only thing that changes is that his
- slope would now be negative 3 instead of
- negative 2 so we would still have the
- same y-intercept
- all right he still starts at 240 but
- let's get a couple different points we
- can change the graph after 5 weeks well
- y equals a negative 3 times 5 plus 240
- that gives me 225 and at let's go 10
- weeks
- so y equals negative 3 times 10 plus 240
- that gives me 210 so I can graph these
- three on and I will switch to a blue to
- graph these so we're still at zero 240
- at 5 weeks or at 225 we said which isn't
- here and that 10 weeks here at 210 so
- you can see that this graph is a little
- bit different he will reach his
- weight-loss plant goal in 20 weeks
- instead of 30 if he ups it to 3 pounds a
- week and I think that is the end of our
- plan yeah
- there you go
-
in this video we are going to work on
Toggle Transcript
