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Parallel lines from equation (example 2) | Mathematics I | High School Math | Khan Academy

Video vocabulary

know

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US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

see

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US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

negative

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US / 'neɡətɪv /

UK / ˈnɛɡətɪv /

A2
  • adjecitve
  • Being harmful, unwanted or unhelpful
  • In mathematics, being less than zero
  • Focusing on the bad aspects; pessimistic
  • noun
  • The opposite to a positive electrical charge
  • In grammar, containing words such as 'no' or 'not'
  • Reply to a question or statement that means 'no'
  • Image on camera film used to make a photo

parallel

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US / 'pærəlel /

UK / ˈpærəˌlɛl /

B1
  • adjecitve
  • (Of two lines) at equal distance from each other
  • (Of computer operation) happening at the same time
  • Very similar and often occurring at the same time
  • noun
  • A line on a map a set distance from the equator
  • verb
  • To be equal to, or like, something else
  • To compare

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

with

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US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

case

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US / keɪs /

UK / kes /

A1
  • noun
  • Container used to carry things, e.g. clothes
  • Set of facts about a crime
  • Set of facts about an event
  • Example or instance of something
  • verb
  • To find out about a place, as in planning to steal

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

different

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US / ˈdɪfrənt /

UK / ˈdɪfrənt /

A1
  • adjecitve
  • Not of the same kind; unlike other things

care

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US / keə(r) /

UK / kɛr /

A1
  • noun
  • Treatment you receive for your health or safety
  • Something that a person worries about
  • verb
  • To feel interest, concern, or worry
  • To look after someone or something

about

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US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

own

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US / əʊn /

UK / on /

A1
  • adjecitve
  • Belong to oneself
  • determiner
  • Yours, his, hers, etc.; not belonging to another
  • pronoun
  • (Something) belong to myself
  • verb
  • To have something as your property

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

most

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US / məʊst /

UK / most /

A1
  • adverb
  • Very; extremely
  • Greatest possible degree
  • pronoun
  • Nearly all of something

out

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US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

minus

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US / ˈmaɪnəs /

UK / ˈmaɪnəs /

A2
  • adjecitve
  • Being close to the bottom of a letter grade
  • noun
  • Negative quality; disadvantage
  • Sign that indicates subtraction
  • preposition
  • Being less than zero in number
  • Used when subtracting one number from another
  • verb
  • To take one number away from another; subtract

form

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US / fɔ:m /

UK / fɔrm /

A1
  • noun
  • Sports team or person's current winning record
  • Document you complete when making an application
  • Visible shape or style; type; kind
  • verb
  • To organize something such as a club or group
  • To develop; to come into a shape or substance
  • To make something into a particular shape

from

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US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

leave

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US / li:v /

UK / liv /

A1
  • noun
  • Permission to do something
  • Vacation time; time off work
  • verb
  • To go away from; depart
  • To gift property to someone after you die
  • To allow something to continue happening
  • To let something remain unused or available
  • To let something or someone remain somewhere

another

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US / əˈnʌðə(r) /

UK / əˈnʌðɚ /

A1
  • adjecitve
  • One more, but not this
  • determiner
  • One more added
  • pronoun
  • One more (thing)

guy

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US / ɡaɪ /

UK / ɡaɪ /

A1
  • noun
  • Man; boy; any person

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

relevant

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US / ˈreləvənt /

UK / ˈrɛləvənt /

A2
  • adjecitve
  • Having an effect on an issue; related or current

any

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US / 'enɪ /

UK / ˈɛni /

A1
  • adjecitve
  • One, or some, no matter which
  • pronoun
  • One (thing) of many; some

those

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US / ðəʊz /

UK / ðoz /

A1
  • determiner
  • The people or things we are talking about
  • pronoun
  • The objects far from the speaker

line

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US / laɪn /

UK / laɪn /

A1
  • noun
  • Border that divides two places or regions
  • Long crease in the skin, often from age
  • Mark that is long, straight and very thin
  • Row of words, letters or numbers that are written
  • Telephone connection
  • People waiting one behind the other; queue
  • Long thin wire, e.g. for electrical signal
  • verb
  • To put material along the inside of something

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

for

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US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

equation

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US / ɪˈkweɪʒn /

UK / ɪˈkweʒən, -ʃən /

B1
  • noun
  • Mathematical statement showing things to be equal
  • Complex set of different facts, ideas or issues

exact

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US / ɪɡ'zækt /

UK / ɪɡˈzækt /

A2
  • adjecitve
  • Completely correct; accurate; specific
  • verb
  • To get something, sometimes using force

standard

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US / 'stændəd /

UK / ˈstændəd /

A2
  • adjecitve
  • Being the accepted normal level of quality
  • (Of a language) being the most accepted in a place
  • noun
  • Official unit of measuring something
  • Principle of behaving in a moral way

positive

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US / ˈpɒzətɪv /

UK / ˈpɑzɪtɪv /

A2
  • adjecitve
  • Showing agreement or support for something
  • Being sure about something; knowing the truth
  • Having the charge produced by electrons
  • Being good or useful
  • Showing that a chemical is present in a test

slope

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US / sləʊp /

UK / sloʊp /

B1
  • noun
  • Angle of a decline, e.g. where a road dips down
  • Surface on which people can ski
  • verb
  • To have one end that is not as high as the other

definitely

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US / ˈdefɪnətli /

UK / ˈdefɪnətli /

A2
  • adverb
  • Without question; beyond doubt

three

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US / θri: /

UK / θri /

A1
  • number
  • Number 3

term

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US / tɜ:m /

UK / tɚm /

A1
  • noun
  • Conditions applying to an agreement, contract
  • Length of time something is expected to happen
  • Fixed period of weeks for learning at school
  • The (precise) name given to something
  • verb
  • To call; give a name to

than

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US / ðən /

UK / ðən /

A1
  • conjunction
  • Used to compare two things that are not equal

one

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US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

other

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US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

into

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US / 'ɪntə /

UK / ˈɪntu /

A1
  • preposition
  • Moving or going inside something
  • In the same direction as; in the direction of
  • So as to become; taking the state of

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

kind

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US / kaɪnd /

UK / kaɪnd /

A1
  • adjecitve
  • In a caring and helpful manner
  • friendly and considerate
  • noun
  • One type of thing

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

four

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US / fɔ:(r) /

UK / fɔr, for /

A1
  • number
  • 4

divide

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US / dɪ'vaɪd /

UK / dɪˈvaɪd /

A2
  • verb
  • To split numbers by another number, e.g. 6 / 2 = 3
  • To separate something into equal pieces

already

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US / ɔ:lˈredi /

UK / ɔlˈrɛdi /

A1
  • adverb
  • Having happened or been done before this time

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

either

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US / ˈaɪðə(r) /

UK / ˈiðɚ, ˈaɪðɚ /

A1
  • adjecitve
  • One of two (used when there is a choice of two)
  • adverb
  • (After negative statements) likewise, in addition
  • conjunction
  • Used as the first of two connected things
  • determiner
  • Used as the first of two connected things
  • pronoun
  • The one or the other

point

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US / pɔɪnt /

UK / pɔɪnt /

A1
  • noun
  • An item to be discussed
  • Small spot or dot
  • Fact or detail
  • Feature of something
  • The size of the text on a page or screen
  • A certain time or stage in a process
  • Certain position in time or space
  • Idea or fact you try to convince people about
  • Measurement of scores in a game, sport
  • Sharp end of something, e.g. a pen or pin
  • verb
  • To face a certain direction, e.g. north
  • To indicate something with your finger to others

side

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US / saɪd /

UK / saɪd /

A1
  • adjecitve
  • In addition to the central or most important thing
  • Next to, or very close to, the right or left of
  • noun
  • Position or opinion that is opposite to another
  • Right or left part of a person's body
  • Feature of someone's personality
  • Straight edge of an object
  • One of two or more groups fighting each other
  • verb
  • To decide to agree with one point, not the other

plus

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US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

importantly

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US / ɪmˈpɔːtntli /

UK / ɪmˈpɔːrtntli /

A2
  • adverb
  • In an important way;

really

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US / ˈri:əli /

UK / ˈriəˌli, ˈrili /

A1
  • adverb
  • Used to stress something that is said; definitely
  • In a true or accurate manner
  • Very

pick

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US / pɪk /

UK / pɪk /

A1
  • noun
  • Sharp tool used for breaking the ground
  • Item selected from a group of choices
  • verb
  • To take fruit or vegetables from a plant or tree
  • To decide on a thing from various choices; select
  • To remove (flower, etc.) with your fingers

compare

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US / kəm'peə(r) /

UK / kəmˈpɛr /

A1
  • verb
  • To consider how similar and different things are

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

same

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US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

whole

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US / həul /

UK / hol /

A1
  • adjecitve
  • Complete or full; all of
  • Being in a good condition
  • noun
  • Complete amount or sum; total

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

equal

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US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

cancel

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US / 'kænsl /

UK / ˈkænsəl /

A2
  • verb
  • To end a legal, business, or other agreement
  • To stop a planned event from happening

add

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US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

both

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US / bəuθ /

UK / boθ /

A1
  • determiner
  • Used to refer to two things at the same time
  • pronoun
  • Used to refer to two things at the same time

very

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US / 'verɪ /

UK / ˈvɛri /

A1
  • adjecitve
  • Concerning a large degree or amount
  • adverb
  • A lot; much; many
  • Used to stress or emphasize a noun

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

everything

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US / 'evrɪθɪŋ /

UK / ˈɛvriˌθɪŋ /

A1
  • pronoun
  • All of the things mentioned

their

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US / ðɛː /

UK / ðer /

A1
  • determiner
  • Belonging to them

way

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US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

move

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US / mu:v /

UK / muv /

A1
  • noun
  • Act of moving a playing piece in chess, etc.
  • An action; doing something
  • Step taken to achieve a goal
  • verb
  • To cause someone to have certain emotions
  • To cause something to change to a different place
  • To change where people live or a business operates
  • To take action to do or achieve something

figure

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US / ˈfiɡə /

UK / ˈfɪɡjɚ /

A1
  • noun
  • Your body shape
  • Numbers in a calculation
  • Doll-like thing meant to represent a person
  • Picture or diagram giving information in a text
  • Person who is very important or famous
  • Shape of a person seen indistinctly or in outline
  • Amount that is expressed in numbers
  • verb
  • To appear in a game, play or event
  • To calculate how much something will cost
  • To understand after thinking; work out

its

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US / ɪts /

UK / ɪts /

A1
  • adjecitve
  • Referring to or belonging to ‘it’
  • determiner
  • Of something; belonging or related to something
  • other
  • Possessive form of “it”
  • Subtitles section
  • We have three lines and we have to figure out which of the three are parallel.
  • So line A-- and it can't be parallel on its own, it has to be parallel to another of the three lines.
  • So the equation for line A is y is equal to 3/4 x minus four.
  • Line B is 4y minus 20 is equal to negative 3x.
  • And then line C is negative 3x plus 4y is equal to 40.
  • So to figure out if any of these lines are parallel to any of the other lines, we just have to compare their slopes.
  • If any two of these lines have the same slope and they're different lines, they have different y-intercepts, then they're going to be parallel.
  • Now line A, it's very easy to figure out its slope.
  • It's already in slope-intercept form.
  • This is mx plus b, the slope is 3/4 and the y-intercept, which isn't as relevant when you're figuring out parallel lines, is negative 4.
  • So let's see what the other character's slopes are.
  • This isn't in any kind of standard form.
  • It's not a standard form, slope-intercept, or point-slope form, but let's see what the slope of this line is.
  • So to get it into slope-intercept form, which is really the easiest one to pick out the slope from, let's add 20 to both sides of this equation.
  • The left-hand side, those cancel out, that was the whole point, you get 4y is equal to negative 3x plus 20.
  • And now we can divide everything by 4.
  • We are left with y is equal to negative 3/4 x plus 5.
  • So in this case, y-intercept is 5, but most importantly, the slope is negative 3/4, so it's different than this guy.
  • This is negative 3/4, this is positive 3/4, so these two guys definitely aren't parallel.
  • Let's move on of this guy in standard form.
  • So let's get the x term on the other side.
  • So let's add 3x to both sides of this equation.
  • Left-hand side, these cancel out.
  • We're just left with 4y is equal to 3x plus 40, or 40 plus 3x, either way.
  • Now we can divide both sides by 4 you have to divide every term by 4.
  • The left-hand side, you're left with y.
  • The right-hand side, you have 3/4 x plus 10.
  • So here, our slope is 3/4 and our y-intercept, if we care about it, is 10.
  • So this line and this line have the exact same slope, 3/4, and they're different lines because their y-intercept is different.
  • So we know that A and C are parallel lines and B is not parallel to either one of the other two.