S5 Mathematics
Coordinate Geometry
Equation of straight line
Lam Shek Ki
(Po Leung Kuk Mrs. Ma Kam Ming-Cheung Foon Sien College)
Main ideas



Abstraction through nominalisation
Making meaning in mathematics through:
language, visuals & the symbolic
The Teaching Learning Cycle
Content(According to CG)
S1 to S3
 Distance between two points.
 Coordinates of mid-point.
 Internal division of a line segment.
 Polar Coordinates.
 Slope of a straight line.
Content(According to CG)
S5
 Equation of a straight line
 Finding the slope and intercepts from the
equation of a straight line
 Intersection of straight lines
 Equation of a circle
 Coordinates of centre and length of radius
Direct instruction
Given any straight line,
there is an equation so
that the points lying on
the straight line must
satisfy this equation,
this equation is called
the equation of the
straight line. …
Why?
How?
Wha
t?
A point
lying on
the line
A point
not lying
on the line
Points lying on the straight line
Pack in
(x, y) : symbolic representation of a point
x-coordinate
nominal group 
y-coordinate
3x+2y=5
(Equation of a straight line)
Problems
Some students :
- do not understand “x” means “x-coordinate”
- cannot accept “x = 2” represents a straight line.
- don’t know why the point-slope form can help to
find the equation
-……
A point
lying on
the line
A point
not lying
on the line
Unpack
Points lying on the straight line
(x, y) : symbolic representation of a point
x-coordinate
nominal group 
y-coordinate
3x+2y=5
(Equation of a straight line)
A point
LANGUAGE
language
& visual
language
& symbolic
LANGUAGE
VISUAL &
SYMBOLIC
VISUAL
SYMBOLIC
visual &
symbolic
(x, y)
Unpack the meaning of Equation of straight line
by
guessing the common feature of the
points lying on the straight line.
y
5
xy
4
(-2,3)
(-5,2)
-6
-5
-4
-3
L1
-2
(-2,-2)
-1
3
(3,3)
2
x=y
1
(1,1)
0
1
-1
-2
-3
-4
-5
2
x
3
4
5
6
7
(x,y)
x-coordinate = y-coordinate
y
5
xy
4
3
(-2,3)
-5
(3,3)
2
(-5,2)
-6
L1
-4
-3
-2
(-2,-2)
-1
1
(1,1)
0
1
-1
-2
-3
-4
-5
2
x=y
x
3
4
5
6
7
(x,y)
x-coordinate = y-coordinate
y
5
xy
4
(-2,3)
(-5,2)
-6
-5
-4
-3
L1
-2
(-2,-2)
-1
3
(3,3)
2
x=y
1
(1,1)
0
1
-1
-2
Visual representation
of “lying …” and “not
lying…”
-3
-4
-5
2
x
3
4
5
6
7
(x,y)
x-coordinate = y-coordinate
y
5
L2
4
(-1,3)
-5
-4
-3
x+y 2
x + y=2
2
(-3,2)
-6
3
-2
-1
1
(1,1)
0
1
-1
-2
2
x
3
4
5
(x,y)
(4,-2)
-3
The sum of x-coordinate and y-coordinate is 2
-4
-5
6
7
Mathematical concepts
Setting the
context
Students constructing
independently
Teacher modelling
and deconstructing
Teacher and students
constructing jointly
Developing a mathematical concepts
y
5
4
x - y=3
L3
(x,y)
3
2
1
-6
-5
-4
-3
-2
-1
0
-1
-2
(-1,-4) -3
-4
-5
1
2
(4,1)
3 4 5
(2,-1)
x
6
7
Findings

For every straight line, the coordinates of
the points on the straight line have a
common feature.
Express that feature mathematically
Equation of the straight line

Moreover, the coordinates of the points
that do not lie on the straight line do not
have that feature.
Abstraction through nominalisation
x-coordinate

x
common feature
 Equation of
of straight line Abstractionstraight line
A point having
the feature

The coordinates
satisfy the equation
Vertical lines
(-3 , 2)
The x-coordinate of any point
lying on the straight line is -3.
Equation:
x = -3
y
5
L5
4
x =-3
3
2
(-3,2)
1
-6
-5
-4
-3 -2 -1
(-3,0)
0
x
1
2
3
4
-1
-2
The x-coordinate is -3
(-3,-3)
-3
-4
-5
5
6
7
y
5
4
y =2
3
2
(-3,2)
L4
(1,2)
(3,2)
1
-6
-5
-4
-3
-2
-1
0
(x,y)
1
2
3
-1
The y-coordinate is 2
-2
-3
-4
-5
4
5
x
6
7
Horizontal line
(3, 2)
The y-coordinate of any point
lying on the straight line is 2
Equation:
y=2
Conclusion
Indentify and unpack the nominal groups
 Experience the process of abstraction
 Make use of the meaning-making system
in mathematics
 Scaffolding : The teaching learning cycle
Thank you!