Line equations

Season 01 • Episode 16 • Line equations

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Line equations

Season 01 Episode 16 Time frame 55 mins

Prerequisites :

^{Basialgebraskills.}

Objectives :

•

^{Understand how anequation denes alinebut also regionsof the plane.}

•

^{Pratise some} omputationswith lineequations.

Materials :

•

^Slideshow.

•

^{Equation and listof pointsfor eahteam.}

1 – Find the right points 25 mins

Thegroupisdividedinto4teams.Eahteamisgivenalineequationandalistof20point

oordinates (the same for every team). One memberof eah team goesto the board. He

or she willplae points ona oordinategraph aording tothe instrutionof the team.

•

^{Turn by turn, eah team piks a pair of oordinates in the list and says it out loud.}

These are the oordinates of apoint in the oordinategraph.

•

^{Everyteam omputes the resultof its algebraiexpression with the oordinates given.}

If the result is

•

^{equalto zero,the team plaesthe pointon the graph with a red ross;}

•

^{negative, the team plaes the point onthe graphwith a blue ross;}

•

^{positive, the team plaes onthe graph with agreen ross.}

The rst teamto havethree pointsof eah olourwins and the gamestops.

Sores are then omputed in the following way :

•

^{Three points forevery red point.}

•

^{Two points for every blue orgreen point.}

2 – Speed contest 25 mins

Eah team is given a listof equations. Foreah equation,they have to nd :

•

^{the oordinates ofthree pointson the set dened by this equation;}

•

^{the shape of the set.}

They an study the equations inthe order they want.

The rst teamto give the orret answers about one equation wins 5 points.

3 – Grading End of session

At the end of the session,the team with the most pointsgets anA

⋆

, the seondteam an

Line equations

Season 01 Episode 16 Document Team 1

Your expression :

− 2x + 6y − 6

^.

Twenty pairs of oordinates.

( − 2, 3) (1, 1) (4, − 1) (3, 2) (0, 1) ( − 3, 0) ( − 4, − 1) ( − 1, 1) (2, 3) (0, 2) (1, 4) ( − 2, − 2) ( − 4, 2) (2, − 2) ( − 2, 5) (5, 4) (4, 1) (1, − 1) ( − 3, 1) (0, − 1)

Line equations

Season 01 Episode 16 Document Team 2

Your expression :

4x − 6y + 10

^.

Twenty pairs of oordinates.

( − 2 , 3) (1 , 1) (4 , − 1) (3 , 2) (0 , 1)

( − 3, 0) ( − 4, − 1) ( − 1, 1) (2, 3) (0, 2)

(1, 4) ( − 2, − 2) ( − 4, 2) (2, − 2) ( − 2, 5)

(5, 4) (4, 1) (1, − 1) ( − 3, 1) (0, − 1)

Line equations

Season 01 Episode 16 Document Team 3

Your expression :

4x − 2y + 4

^.

Twenty pairs of oordinates.

( − 2, 3) (1, 1) (4, − 1) (3, 2) (0, 1) ( − 3, 0) ( − 4, − 1) ( − 1, 1) (2, 3) (0, 2) (1, 4) ( − 2, − 2) ( − 4, 2) (2, − 2) ( − 2, 5) (5, 4) (4, 1) (1, − 1) ( − 3, 1) (0, − 1)

Line equations

Season 01 Episode 16 Document Team 4

Your expression :

2x + 3y − 5

^.

Twenty pairs of oordinates.

( − 2 , 3) (1 , 1) (4 , − 1) (3 , 2) (0 , 1)

( − 3, 0) ( − 4, − 1) ( − 1, 1) (2, 3) (0, 2)

(1, 4) ( − 2, − 2) ( − 4, 2) (2, − 2) ( − 2, 5)

(5, 4) (4, 1) (1, − 1) ( − 3, 1) (0, − 1)

Line equations

Season 01

Episode 16

Document 15 equations

For eah equation nd out :

•

^{the oordinates of three points on the set dened by this equation;}

•

^{the shape of the set.}

You an study the equations in the order you want.

Whenever you think you have a omplete answer, all the teaher to hek

and win 5 points if it's right.

x ² + y ² − 1 = 0 3 x − y + 2 = 0 2 x ² + y = 0 xy = 6 − x + 4 y = 0 y − √

x = 2 x + y = 7 √

x + 2 = 6 − 3 x − y − 7 = 0 x ² − y ² = 5 − ^x ₂ − 2 y = 0 − ⁴ _x − 2 y = 0

− 2 x ² − y − 7 = 0 ¹

x + ¹

y = 0 − x − y + 1 = 0

Line equations

Season 01

Episode 16

Document 15 equations

For eah equation nd out :

•

^{the oordinates of three points on the set dened by this equation;}

•

^{the shape of the set.}

You an study the equations in the order you want.

Whenever you think you have a omplete answer, all the teaher to hek

and win 5 points if it's right.

x ² + y ² − 1 = 0 3 x − y + 2 = 0 2 x ² + y = 0 xy = 6 − x + 4 y = 0 y − √

x = 2 x + y = 7 √

x + 2 = 6 − 3 x − y − 7 = 0 x ² + y ² = 5 − ^x ₂ − 2 y = 0 − ⁴ _x − 2 y = 0

− 2 x ² − y − 7 = 0 ¹

x + ¹

y = 0 − x − y + 1 = 0