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Slope of Perpendicular Line

Video vocabulary

their

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US / ðɛː /

UK / ðer /

A1
  • determiner
  • Belonging to them

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

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

bit

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US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

take

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US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

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

subtract

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US / səbˈtrækt /

UK / səbˈtrækt /

B2
  • other
  • To take away a value or amount from another
  • verb
  • To take away a value or amount from another

prove

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US / pru:v /

UK / pruv /

A2
  • verb
  • To demonstrate truth by providing evidence

they

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US / ðeɪ /

UK / ðe /

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

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

reciprocal

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US / rɪˈsɪprəkl /

UK / rɪˈsɪprəkəl /

C1
  • adjecitve
  • Equal and meeting the needs of both sides

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)

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’

mean

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US / mi:n /

UK / min /

A1
  • adjecitve
  • Being good at
  • Nasty; unkind
  • Not liking to spend money; cheap; stingy
  • noun
  • Average of a set of numbers
  • verb
  • To express a particular idea or thought
  • To intend to do something in particular
  • To have a particular meaning or value

solve

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US / sɒlv /

UK / sɑ:lv /

A2
  • verb
  • To figure out a way to handle a difficult problem

like

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US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

down

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US / daʊn /

UK / daʊn /

A1
  • adjecitve
  • Being sad, sick, or unhappy
  • Not operating, working, or functioning as expected
  • adverb
  • In a sitting or lying position
  • Towards or on the ground, floor, or bottom
  • Written or copied onto a piece of paper or book
  • noun
  • A period of play in American Football
  • The soft, smooth hairs that cover a bird's body
  • preposition
  • Along something's path, course, or direction
  • Going from a higher position to a lower position
  • verb
  • To eat or drink very quickly and without stopping

number

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US / ˈnʌmbə(r) /

UK / ˈnʌmbɚ /

A1
  • noun
  • Symbols such as 1, 2, 56, 793
  • Particular song or dance performed during a show
  • Total quantity or amount of things
  • verb
  • To put numbers on things
  • To assign a sequence within a group, series, set
  • To claim to be part of a larger group, series, set

find

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US / faɪnd /

UK / faɪnd /

A1
  • noun
  • Object discovered by chance
  • Things that have been discovered from searching
  • verb
  • To become aware of something that is happening
  • To discover or meet by chance
  • To decide if someone is guilty of a crime, or not
  • To learn through study, research, or effort
  • To discover something by looking for it

different

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US / ˈdɪfrənt /

UK / ˈdɪfrənt /

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

each

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US / i:tʃ /

UK / itʃ /

A1
  • determiner
  • Every one of two or more things
  • pronoun
  • Per one person or thing

purple

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US / 'pɜ:pl /

UK / ˈpɚpəl /

A1
  • adjecitve
  • Being a color that is a mixture of red and blue

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

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

write

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US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

obviously

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US / ˈɒbviəsli /

UK / ˈɑːbviəsli /

A2
  • adverb
  • In a way that is obvious/easy to see or understand

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

third

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US / θɜ:d /

UK / θɜ:rd /

A1
  • adjecitve
  • 3rd: Number after second

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

will

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US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

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

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

intersect

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US / ˌɪntə'sekt /

UK / ˌɪntɚˈsɛkt /

B2
  • verb
  • To divide something by crossing it

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

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

half

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US / hɑ:f /

UK / hæf, hɑf /

A1
  • adjecitve
  • Not complete
  • adverb
  • Partly; somewhat
  • noun
  • One of two equal periods of game time in a sport
  • The part you get when one is divided into two;

make

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US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

inverse

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US / ɪnˈvɜ:s /

UK / ˈɪnˌvə:s /

B2
  • adjecitve
  • Being the opposite of something else
  • noun
  • Thing that is the complete opposite of another

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

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

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

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

review

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US / rɪˈvju: /

UK / rɪˈvju /

A2
  • noun
  • Examination of soldiers and supplies
  • Opinion, as in a paper, about movie, book, or play
  • Studying again to remind yourself about something
  • verb
  • To carefully look at the quality of something
  • To formally examine something in the military
  • To write an opinion about movie, book, or play
  • To study again to remind yourself about something

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

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

from

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US / frəm /

UK / frʌm, frɑm,frəm /

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

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

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

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

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

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

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

put

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US / pʊt /

UK / pʊt /

A1
  • phrasal verb
  • to make a light stop shining by pressing or moving a switch
  • verb
  • To move or place a thing in a particular position
  • To rate something in importance or value
  • To write or say something in a certain manner

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

angle

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US / ˈæŋgl /

UK / ˈæŋɡəl /

B1
  • noun
  • Place where two lines or surfaces meet

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

video

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US / 'vɪdɪəʊ /

UK / ˈvɪdiˌo /

A2
  • adjecitve
  • Of a moving film, with sound
  • noun
  • Recording capturing action with sound
  • verb
  • To make a moving film of, with sound

but

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US / bət /

UK / bʌt,bət /

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

apply

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US / ə'plaɪ /

UK / əˈplaɪ /

A1
  • verb
  • To spread a substance or liquid over a surface
  • To commit your time and effort to doing something
  • To make something useful in a certain situation
  • To be relevant for a situation
  • To ask formally for (job, permission etc.)

become

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US / bɪ'kʌm /

UK / bɪˈkʌm /

A1
  • verb
  • To begin to be; grow to be; develop into
  • To be suitable for a particular job or role

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

not

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US / nɒt /

UK / nɑt /

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

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

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

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

for

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US / fə(r) /

UK / fɔr,fə /

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

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

magenta

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US / məˈdʒentə /

UK / məˈdʒɛntə /

C1
  • noun
  • Deep purplish red

perpendicular

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US / ˌpɜ:pənˈdɪkjələ(r) /

UK / ˌpə:pənˈdɪkjəlɚ /

C1
  • adjecitve
  • Being at right angles to a given line or plane

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

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)

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

green

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US / gri:n /

UK / ɡrin /

A1
  • adjecitve
  • Color of young leaves
  • Covered with vegetation, e.g. grass
  • Concerned about protecting the environment
  • The color of young leaves
  • Lacking in experience/knowledge due to being young
  • Being not fully grown or ripe, as in fruit
  • noun
  • Large grassy area
  • used as a part of a name of a place (UK)
  • Subtitles section
  • Find the slope of a line perpendicular to the line 3x plus 2y is equal to 6. Now just as a bit of a review, let's just think about two lines that are perpendicular.
  • So that's my x-axis, this is my y-axis, my y-axis.
  • And let's say I have one line over here just like that.
  • And let's say that it has a slope.
  • Let's say that the slope over here for this line is equal to m.
  • Now let's have a line that's perpendicular to that line.
  • So that means it intersects at a 90 degree angle.
  • So let's say this line right here is perpendicular, so this right here is a 90 degree angle.
  • Then if this purple line has a slope of m, then this green line will have a slope of negative 1 over m.
  • It is the negative reciprocal or the negative inverse of the slope of the magenta line.
  • And this is obviously the negative inverse of the green line.
  • Their slopes are the negative inverse of each other, and that's what makes them perpendicular.
  • And I won't prove it in this video.
  • But let's just apply that to this right over here.
  • So we have a line 3x plus 2y is equal to 6. If we figure out this line's slope, then the slope of a line that's perpendicular to it will be the negative reciprocal of that slope.
  • So let's find this guy's slope, and then the negative reciprocal of that will be the slope of a line that's perpendicular to it.
  • So we have 3x plus 2y is equal to 6. The easiest way to find the slope is to put this equation in slope-intercept form, or y is equal to mx plus b form.
  • So we want to solve for y.
  • Let's subtract 3x from both sides.
  • So we subtract 3x from both sides.
  • And so the left-hand side, we're just left with 2y.
  • And on the right, we're left with, we could write this as 6 minus 3x or negative 3x plus 6. Now we can divide both sides of this equation by 2.
  • So divide by 2, divide by 2, divide by 2. The left-hand side, we just have a y is equal to negative 3 halves x plus 6 over 2 is 3. So the slope of this line, we now wrote it in slope-intercept form.
  • This right here is our slope.
  • This right here is our m.
  • The slope of this line is negative 3 halves.
  • M is equal to negative 3 halves.
  • So the slope of a line that's perpendicular to this line will be the negative reciprocal of this.
  • So if we take, let me write it down.
  • So slope of perpendicular line is going to be the negative reciprocal.
  • So this is a negative number already.
  • If we take the negative of that, it's going to become a positive number.
  • And then we have the reciprocal.
  • Instead of 3 halves, we will have 2 thirds.
  • So they're different signs, and this is a reciprocal of that.
  • And we are done.