Real Life Linear Equations

Summary

In 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

00:00

📘 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.

05:00

📊 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.

10:01

📚 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.

15:04

🎉 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.

Keywords

💡Linear Equations

Linear equations are algebraic equations that represent a straight line when graphed. In the context of the video, linear equations are used to model real-life situations where there is a direct proportionality between two variables. The video emphasizes the use of the slope-intercept form of a linear equation, y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

💡Word Problems

Word problems are practical, real-world scenarios presented in narrative form that require mathematical solutions. The video script discusses the importance of translating word problems into mathematical equations. These problems are integral to the video's theme as they demonstrate how linear equations can be applied to solve everyday situations.

💡DESK Method

The DESK method is a problem-solving strategy introduced in the video to tackle word problems involving linear equations. It stands for Define, Equation, Solve, and Complete Sentence. The method guides viewers through the process of identifying variables, setting up equations, solving for the unknown, and then presenting the answer in a clear, complete sentence.

💡Variables

In the video, variables are placeholders for values that can change within an equation. The 'D' in DESK stands for 'Define your variables,' which is crucial for setting up a linear equation. Variables like 'X' and 'Y' are defined in relation to the context of the word problem, with 'X' often representing an independent variable that can be chosen or changed.

💡Dependent Variable

The dependent variable, represented by 'Y' in the video, is the outcome that is dependent on the value of the independent variable. It is a key concept in linear equations, as it is the value that the equation is solving for. In the context of the video, the dependent variable is what changes in response to the independent variable.

💡Independent Variable

The independent variable, symbolized by 'X', is a variable that can be freely chosen without being determined by other variables in the equation. The video explains that the independent variable is the one that we control or change, and the dependent variable will change accordingly.

💡Slope (M)

Slope, denoted by 'M' in the slope-intercept form of a linear equation, represents the rate of change between two variables. In the video, the slope is described as how much the dependent variable 'Y' changes for each unit change in the independent variable 'X'. It is a fundamental concept in linear equations, illustrating the proportional relationship between variables.

💡Constant (B)

The constant, or 'B' in the equation y = mx + b, represents a fixed starting value in the context of the word problems discussed in the video. It is the initial amount or value that does not change as the independent variable varies. The video uses the constant to establish the baseline from which changes are measured.

💡Real-life Examples

Real-life examples are used throughout the video to demonstrate how linear equations can model various scenarios, such as saving money in a retirement account or accumulating books in a library. These examples serve to illustrate the practical application of the mathematical concepts being taught, making the abstract ideas more concrete and relatable.

💡Complete Sentence

A complete sentence, as part of the 'C' in the DESK method, is emphasized in the video as the proper way to present the solution to a word problem. It involves not just stating the numerical answer but also explaining the context and the variable it represents, ensuring that the solution is clear and understandable.

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