Different types of line equations

Season 01 • Episode 17 • Different types of line equations

Different types of line equations

Season 01

Episode 17 Time frame 55 mins

Prerequisites :

Objectives :

•

•

Materials :

•

•

•

The lass is divided into four teams. Eah team is given an answer sheet where answers

willbewrittenfor the threeparts. The two rst parts are turnby turngames. The thrid

part is a speed game.

1 – Recognize a form 20 mins

Turn by turn,eah teamis given (orally)an equationand has tond out what typeit is

and win pointsforeverygoodanswer. Ifateam givesawrong answer, the next teaman

answerand win 3points,and so on.

∆ ¹ y = − 4x ∆ ^{2 x}

− 2 + ^y 5 = 1

∆ ³ 7x + 3y − 8 = 0 ∆ ⁴ y − 5 = − 3(x − 2)

∆ ^{5 x 1}

3

+ ^y

− 3 = 1 ∆ ⁶ x + √

5y − 3 = 0

∆ ⁷ y + 1 = − ¹ 2 (x + 5) ∆ ⁸ y = − 7(x + 8)

2 – Switch from one form to another 25 mins

Four lineequationsaregiven. Teamshave10minutesorsotoonvert theseequationsto,

the threeotherforms.Teamsarethen askedtollone line,turnbyturn,one lineforeah

team. Four points are awarded for every good answer. If a team gives a wrong answer,

the next team an answerand win 3 points,and soon.

Generalform Slope-interept form Point-interept form Interept form

d 1 ⋆ 3x − 3y + 3 = 0 y = x + 1 y + 1 = 1(x − ( − 2)) ^x

− 1 + ^y ₁ = 1 d 2 x − y − 3 = 0 y = x − 3 y − 0 = 1(x − 3) ⋆ ^x ₃ + ^y

− 3 = 1 d 3 2x + 5y − 10 = 0 y = − ² 5 x + 2 y − 0 = − ² 5 (x − 5) ⋆ ^x ₅ + ^y 2 = 1 d 4 6x − y − 11 = 0 ⋆ y = 6x − 11 y − 1 = 6(x − 2) ^{11 x}

6

+ ^y

− 11 = 1

3 – Computations – Speed game Remaining time.

Four questions are asked about the lines in the previous part. The rst team to rise all

theirhandsananswerandget10points.Iftheansweriswrong,anotherteamandanswer

Season 01 • Episode 17 • Different types of line equations

1. Drawthe lines

d 1

d 2

2. Find two points oneah of the lines

d 3

d 4

3. Compute the

x

d 1

d 2

4. Are there two parallellines among these eightlines?

Different types of line equations

Season 01

Episode 17 Document Lesson

Everystraightlinehasaninnitenumberofartesian equations,allequivalentbut some-

times verydierentin the way they lookand the informationthey diretlypresent. Here

are the main kinds of equations. Only the two rst kinds are ommonly used in Frane,

but the othersare quiteinteresting too.

•

ax +by +c = 0

a

b

c

anequationof this form,and indeedmanyas it'salways possibletoapply aoeient

tothe whole equation.

•

y = mx + p

m

p

m

and

p

y

•

y − y 0 = m(x − x 0 )

m

(x ⁰ , y 0 )

is a ouple of real numbers, the oordinates of a point on the line. This form is not

unique, as any point onthe linean beused.

•

x q + y

p = 1

p

q

y

x

It's easy toswithfrom one formto another, as illustrated inthe example below:

4x + 2y − 6 = 0 (General form) 2y = − 4x + 6

y = − 2x + 3 (Slope-intercept form) y = − 2(x − 1) + 1

y − 1 = − 2(x − 1) (Point-slope form) 2x + y = 3

2x 3 + y

3 = 1 x

3 2

+ y

3 = 1 (Intercept form)

Different types of line equations

Season 01

Episode 17

Document Answer sheet

Part 1 – Recognize a form

Line Form

∆ ¹

∆ ²

∆ ³

∆ ⁴

∆ ⁵

∆ ⁶

∆ ⁷

∆ ⁸

Part 2 – Switch from one form to the others

Line General form Slope-interept form Point-slope form Interept form

d 1

d 2

d 3

d 4

Season 01 • Episode 17 • Different types of line equations

Part 3 – Use the best form to carry out a computation

1. Coordinate graph :

1 2 3 4

− 1

− 2

− 3

− 4

− 5

1 2 3 4 5

− 1

− 2

− 3

− 4

− 5

2.

d 3

d 4

3.

d 1

d 2

4. ...