Real Life Linear Equations
Summary
TLDRIn this educational video, the presenter guides viewers through creating real-life linear equations using the DESK method: Define variables, Equation, Solve, and Complete sentence. The focus is on understanding the slope-intercept form (y = mx + b), where 'm' represents the rate of change and 'b' is the starting value. Practical examples, such as saving for retirement and building a book collection, illustrate how to translate word problems into equations and solve for the dependent variable. The video emphasizes the importance of defining variables, setting up equations based on given rates and initial amounts, and solving for specific scenarios, ultimately writing the solution in a complete sentence.
Takeaways
- 📚 The lesson focuses on creating real-life linear equations, particularly using the slope-intercept form (y = mx + b).
- 🔑 The acronym 'DE-SK' is introduced as a method to approach word problems: Define variables, Equation, Solve, and Complete sentence.
- 📈 'D' in DE-SK stands for 'Define', where variables like x (independent) and y (dependent) are assigned to represent different aspects of the problem.
- 📉 'E' in DE-SK stands for 'Equation', where a linear equation is formulated based on the defined variables and the given problem conditions.
- 🔍 'S' in DE-SK stands for 'Solve', which involves substituting the values into the equation to find the solution to the problem.
- ✍️ 'C' in DE-SK stands for 'Complete sentence', emphasizing the importance of providing a clear and full answer to the problem.
- 💡 The lesson uses the terms 'each' and 'per' as indicators to multiply values, and 'starting with' or 'initial amount' as indicators for the constant (b) in the equation.
- 💼 An example is given where Miss Ruddy opens a retirement account with an initial $100 and adds $50 each month, illustrating how to apply the DE-SK method.
- 📚 Another example involves Mr. Lam who starts with 12 books and buys 3 new books each week, further demonstrating the process.
- 📈 The lesson concludes with a challenge for the viewer to apply the DE-SK method to a scenario involving Miss Ruddy's Instagram account, where she gains 7 new followers each day.
Q & A
What does the acronym 'DESK' stand for in the context of solving word problems?
-'DESK' stands for Define, Equation, Solve, and Complete sentence. It helps guide the process of solving word problems by first defining variables, forming an equation, solving it, and then writing the answer in a complete sentence.
What do the variables X and Y represent in linear equations, according to the transcript?
-In linear equations, X is the independent variable, representing something we choose or control, while Y is the dependent variable, representing what we are trying to find, which depends on the value of X.
How is the 'slope' (M) of a linear equation described in the script?
-The slope (M) in a linear equation is described as the change in Y over the change in X. In word problems, M represents how much something changes, such as the rate of increase or decrease.
What does the 'constant' (B) represent in linear equations?
-The constant (B) represents the starting value or initial amount in a word problem. It remains unchanged and is added to the equation to reflect the beginning point.
How do keywords like 'each' or 'per' help when solving word problems?
-Keywords like 'each' or 'per' indicate multiplication in word problems. For example, '20 students per class' suggests multiplying the number of classes by 20.
In the example problem with Ms. Reddy’s retirement account, how is the equation formed?
-The equation is formed as Y = 50X + 100. Here, $50 is added each month (50X) and $100 is the starting amount (constant B).
What is the purpose of writing a complete sentence after solving the equation?
-Writing a complete sentence provides clarity by answering the question in a real-world context, ensuring that the solution is meaningful and understandable, rather than just giving a numerical result.
What equation represents the number of books Mr. Lam has after several weeks?
-The equation representing the number of books Mr. Lam has is Y = 3X + 12, where 3 represents the number of new books added each week and 12 is the initial number of books.
How does the script suggest solving for different values of X, such as 5 weeks or 10 weeks in Mr. Lam’s library example?
-To solve for different values of X, you substitute the desired number of weeks (e.g., X = 5 or X = 10) into the equation Y = 3X + 12 and calculate the total number of books accordingly.
What steps are involved in creating an equation to describe the growth of followers on Ms. Reddy’s Instagram account?
-The steps include defining X as the number of days, Y as the total number of followers, and then creating the equation Y = 7X + 3, where 7 represents the new followers gained each day and 3 is the initial number of followers.
Outlines
📘 Introduction to Real-Life Linear Equations
The speaker begins by introducing the concept of creating real-life linear equations through word problems. The process of solving these problems is encapsulated in the acronym 'DESCRIPT', which stands for Define, Equation, Solve, and Complete Sentence. The speaker emphasizes the importance of identifying variables (X and Y), where X is the independent variable and Y is the dependent variable. The equation 'y = mx + b' is introduced, with 'm' representing the slope and 'b' representing the constant or starting value. The speaker provides examples of how to interpret words like 'each' and 'initial' in the context of setting up equations.
📊 Applying DESCRIPT to a Retirement Savings Scenario
In this section, the speaker applies the DESCRIPT method to a specific scenario where Miss Ruddy opens a retirement account with an initial deposit and plans to add a fixed amount each month. The speaker defines the variables (X as the number of months, Y as the amount of money in the account), sets up the equation (Y = 50X + 100), and solves for the amount of money in the account after 6 and 12 months. The speaker then demonstrates how to write a complete sentence to answer the question, emphasizing the importance of providing context and clarity in the response.
📚 Creating a Library with Weekly Book Additions
The speaker continues with another example, this time involving Mr. Lam who is building a library of books in his classroom. Using the DESCRIPT method, the speaker defines the variables (X as the number of weeks, Y as the total number of books), creates the equation (Y = 3X + 12), and solves for the total number of books after 5 and 10 weeks. The speaker then shows how to write a complete sentence to answer the question, ensuring that the response is both accurate and understandable in a real-life context.
🎉 Conclusion and Encouragement for Practice
The speaker concludes the lesson by summarizing the steps involved in solving word problems using linear equations and encourages viewers to practice these skills. The speaker reiterates the importance of the DESCRIPT method and provides a final example for the viewers to try on their own, involving Miss Ruddy's Instagram account and the number of followers she gains each day. The speaker outlines the steps for this example, leaving the actual solving and sentence completion as an exercise for the viewers.
Mindmap
Keywords
💡Linear Equations
💡Word Problems
💡DESK Method
💡Variables
💡Dependent Variable
💡Independent Variable
💡Slope (M)
💡Constant (B)
💡Real-life Examples
💡Complete Sentence
Highlights
Introduction to creating real-life linear equations using word problems.
Explanation of the DESK method for solving word problems.
The significance of defining variables (D in DESK) in word problems.
The role of the equation (E in DESK) in translating words into a math problem.
The process of solving the equation (S in DESK) to find the desired outcome.
The importance of writing a complete sentence (C in DESK) to answer the problem.
The concept of Y as the dependent variable in a linear equation.
The concept of X as the independent variable that can be chosen or changed.
The role of M in the equation as the slope, representing change.
The role of B in the equation as the constant or starting value.
Key words in word problems that indicate multiplication or constant values.
Example of creating an equation for a retirement account savings problem.
How to define variables in the retirement account example using the DESK method.
Creating the equation for the retirement account using the defined variables.
Solving the retirement account equation to find the amount of money saved over time.
Writing the final answer as a complete sentence for the retirement account example.
Example of creating an equation for a classroom library book collection.
Defining variables for the classroom library book collection using the DESK method.
Creating the equation for the classroom library book collection.
Solving the classroom library book collection equation for a specific number of weeks.
Writing the final answer as a complete sentence for the classroom library example.
Guidance on creating an equation for an Instagram account follower count.
Final summary of the lesson and thanks for watching.
Transcripts
hi everybody today we are going to be
creating real-life linear equations so
today since we're doing real-life linear
equations we are essentially going to be
working with some word problems and
anytime that we're going to do word
problems I'm going to say this phrase
use your desk so des C so desk helps us
remember the process that we're going to
follow every time we have a word problem
so the D in desk is going to stand for
define your variables I want to know in
words what does X represent and what
does Y represent in terms of your word
problem the e in desk represents
equation because after we define our
variables we're going to make an
equation then we're going to do the S
which is to solve so we're going to
solve our equation for whatever they're
asking for and then the C and desk is to
write a complete sentence so we're
always going to answer these word
problems with a complete and thorough
sentence so every time I say use your
desk it means to find your variables
make an equation solve and then complete
sentence okay so today like I said we're
going to be making linear equations from
real-life examples so we're going to be
doing this with y equals MX plus B our
slope intercept form so it is kind of
useful to know what some of these
different variables might represent so
let's start with Y so Y is always going
to be what we are trying to find
what we're trying to find and you also
might call this or you might hear it
called the dependent variable dependent
because this outcome is going to depend
on some other input so our Y is always
going to depend on what we choose for X
which brings us to X so X is what we
choose and we call this the independent
variable and it can be what we choose or
what we change so this is the thing that
we pick and this is what we get out of
it so this is why this is the
independent variable we can pick
whatever we want our Y will depend on
what our X is so that's why they call it
the dependent variable now we still have
M and B so these are going to be things
that we can pull out of our word problem
so B is what we call a constant so a
constant is something that never changes
so you can think of it like that and in
these types of word problems our
constant is going to be our starting
value so anytime we're starting with a
certain amount that's going to be our
constant and we can put that value right
here now M as we know M represents slope
which is change of Y over change of X in
word problems M is going to be how much
we change which kind of makes sense for
the slope because slope is how much you
change going from one point to the next
so we can kind of use these guidelines
to help us look at words and translate
them into a math equation now a few
other key words that I might be useful
to know is anytime you see the word each
or per like Ms ready has 20 students per
class that is going to tell us to
multiply those values and anytime you
see the words starting with or initial
amount that is going to
present that constant value which goes
where our B value is so those are just
little hints that we might use to help
us okay so let's give one of these a try
so we're going to use our desk but
before we do that we're going to read
the equation and I'm going to highlight
some important some important
information so miss ruddy opens a
retirement account and is starting with
$100 so it's I go to a bank and I want
to start saving for retirement so I open
a bank account and this is how much I'm
starting with she plans to add $50 each
month to the account so this is how much
my account is going to change each month
so we want to make an equation that
describes oops that describes the amount
of money in the account each month so
the first thing we're going to do again
the first letter of desk is D which
stands for defining your variables so I
want to know what does X represent and
what does Y represent so remember X
represents the only thing that we can
change in this equation so we can't
change the starting amount we can't
change how much money Miss Reddy is
adding each month but we can change
which month it is or how many months
have gone by so the number of months is
what we're going to pick so that's our
x-value is the number of months now
remember our y-value is always going to
represent what we're trying to find and
we want to describe the amount of money
and they account so that's what our
y-value is going to equal the money in
the account now of course the amount of
money in the account is going to depend
on how many months has gone by so that's
why x is the independent and Y is the
dependent the so to repeat that the
amount of the money in the account
depends on how many months has gone by
so this is the a dependent variable and
this is the independent variable so we
just finished the
d in desc we defined X&Y we define our
variables now the E and s tells us to
make an equation so we know we're going
to use y equals MX plus B now let's
think about what our M value is so
remember M is how much something is
changing so here ICO we're adding $50.00
each month I also want to remind you
each tells us to multiply so we have 50
x months which is represented by X so 50
times X is 50 X now I want to remind you
guys also that that B value is always
going to be our starting amount and it
says them is ready is starting with 100
dollars so we say plus 100 and this is
the equation that we can use to find the
amount of money in the account for
however many months she's been saving so
this kind of makes sense right let's say
I'm saving for 3 months I'm going to do
50 times 3 because I've gone to the bank
3 times and put $50 in but of course I
also have that starting amount of 100
now you might think well why can't I
just solve it like that because if
you're looking way down the line let's
say I'm thinking maybe 50 months from
now you're not gonna want to sit there
and say 50 plus 50 plus 50 plus 50 that
many times so if we can make an equation
to represent the amount of money it
saves us a lot of time so now let's do
the s in desk we want to solve what
they're asking so down here they're
asking how much money does miss Reddy
have after 6 months and then after 12
months
so remember months is represented by X
so we're going to substitute x equals 6
and x equals 12 to help us find our y
value which will represent how much
money so let's substitute x equals 6 so
we have 50 times 6 plus 150 times 6 is
300 plus 100 is 400 and now we're going
to do the same thing except X will equal
12 so 50 times 12
plus 150 times 12 is 600 plus 100 is 700
so this is really nice we have a correct
answer however if someone asked how much
money does miss Reddy have after six
months and you said y equals 400 that
doesn't really make sense in terms of a
real-life problem so we're gonna want to
try to write this answer as a complete
and thorough sentence that answers the
question so how much money does miss
Reddy have after six months we're gonna
start with after six months
miss Reddy has 400 dollars so this is
the kind of complete sentence I would
expect let's answer that second part how
much money does miss Reddy have after
twelve months so we can say after twelve
months
Miss Reddy has 700 dollars and this is
going to be our final answer however we
need to show every step of the way you
need to define your variables make your
equation solve and write a complete
sentence okay let's try one more
together so here mr. Lam wants to create
a library of books in his classroom he
is starting with twelve books he plans
to buy three new books each week create
an equation that describes the number of
books mr. Lam has each week so let's
start by defining our variables so X is
going to be the thing that we control
and the only thing that we can control
is the number of weeks we can say oh
after one week after five weeks after
twenty weeks it doesn't matter
so X represents the number of weeks
that's the thing that we can change Y is
always going to represent what we want
to find and they asked us to describe
the number of books mr. Liam has so Y is
going to run
present the total number of books so
that's the D in dusk we are defining our
variables using real words now we need
to make an equation so we're going to do
y equals so here I can see that the
number of books is changing by three
each week so we can take three and
multiply it by the number of weeks he's
been adding to his library which is 3x
now this is does not represent the total
number of books he has because he
started with some so we have to add that
starting 12 onto the end so remember the
constant is always going to go right
here so the constant is our starting
point which is 12 and our slope is
always going to be how much our value is
changing and it is changing by 3 each
week so that's why we say 3x and this is
the equation that can help us find how
many books mr. lamb has for whatever
number of weeks we want so now let's
figure out how many books does mr. lamb
have after 5 weeks and 10 weeks so this
is the thing that we choose so we're
choosing x equals 5 and x equals 10 and
we're going to substitute to solve for y
so we have 3 times 5 plus 12
we always multiply first so 15 plus 12
which is 27 and then let's substitute x
equals 10 3 times 10 plus 12 here we
have 30 plus 12 which equals 42 now once
again we're always going to write our
final answer as a complete sentence and
it needs to answer the question
thoroughly so how many books does mr.
lamb have after 5 weeks
after 5 weeks
mr. Lam has 27 books and we can do the
same for the second part how many books
does mr. Lam have after 10 weeks we say
after 10 weeks mr. Lam has 42 books okay
go ahead and pause the video and I want
you to give this one a try it says miss
Reddy has created an Instagram account
and started with three followers her mom
her dad and her sister she plans to find
seven new followers each day create an
equation that describes how many
followers she has each day so go ahead
and pause the video and make sure you're
using your desk define make an equation
solve and complete sentence
alright let's go ahead and check so here
X is going to represent the number of
days because that's the only thing that
we can pick and choose and Y is going to
represent what we're trying to find
which is how many followers miss Reddy
has so if we create the equation we
should get y equals 7x plus 3 because
this number is how much change we have
multiplied by the number of days and
this number represents the starting
value which was 3 followers now let's
move on to the s part of desk solving
they asked how many followers will she
have after 10 days so substitute x
equals 10 and 100 days so substitute x
equals 100 last we have to write as a
complete sentence so after 10 days miss
Reddy has 73 followers and after 100
days miss Reddy has 703 followers all
right that is all for today's lesson
thank you so much for watching
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