LU3 System of Equation & Functions
Coordinate of point
Slope / gradient of line
Equation of straight line
System of Equation
Functions
Graphs of Functions
Operations with Functions
Composite Functions
1

If A(-3,4) & B(1,2)
i)
Find the distance between the points
ii) Find the mid-point of AB
Example 1
2

If A(-3,4) & B(1,2)
i)
Find the distance between the points
ii) Find the mid-point of AB
Solution – Example 1
3
47
.
4
5
2
)
5
)(
4
(
20
4
16
)
2
4
(
1
3
2
2
2
2
1
2
2
1
y
y
x
x
3
,
1
2
6
,
2
2
2
2
4
,
2
1
3
2
,
2
2
1
2
1
y
y
x
x

Identify the
gradient
and the
y-intercept
of the
following:-
4
x
y
c
x
y
b
x
y
a
8
1
2
)
(
5
3
1
)
(
3
)
(

Find the gradient of the following coordinates:-
Example 2
a)A (1,3) & B (2,1)
b)A (-2,5) & B (-6,-1)
c) Find the
slope
m
of the line that goes
through the
points
(–2, 5)
and
(3, 5)
.
5

Find the gradient of the following coordinates:-
(a) A(1,3) & B(2,1)
(b) A(-2,5) & B(-6,-1)
Solution - Example 2
6
2
1
2
3
1
1
2
1
2
m
m
x
x
y
y
m
2
3
4
6
2
6
5
1
1
2
1
2
m
m
m
x
x
y
y
m

–2 –1
1
2
3
4
Solution-Example 2c
Find the
slope
m
of the line that goes through the
points
(–2, 5)
and
(3, 5)
.
x
1
= –2
,
y
1
= 5
,
x
2
= 3
,
y
2
= 5;
The slope of a
horizontal line
is
zero
:
y
x
L
6
4
3
2
1
(–2, 5)
(3, 5)
m
= 0
7
2
1
2
1
5
5
0
0
3
( 2)
5
y
y
m
x
x

EXAMPLE
3
Determine whether the following lines
are parallel or perpendicular:-
8
3
6
4
&
0
6
3
2
)
(
x
y
x
y
a
2
2
&
1
2
)
(
x
y
x
y
b

EXAMPLE
3
SOLUTION
Determine whether the following lines are parallel or
perpendicular:-
(a) are Parallel
(b) are perpendicular
(2)(-1/2) = -1
a.
b.
9
3
2
3
6
3
2
0
6
3
2
x
y
x
y
x
y
1
2
1
2
x
y
x
y
4
3
2
3
4
3
4
6
3
6
4
x
y
x
y
x
y
1
2
1
2
2
2
2
x
y
x
y
x
y

Write answers in the
slope-intercept form
:
i)
Passes through (2,5) with the slope of ½
ii)
Passes through (1,-4) and (-5,4)
iii) Perpendicular to the line 2x + y = 3 and
passes through (3,5)
iv) Parallel to the line 2x - 3y = 5 and passes
through (2,-1)
EXAMPLE
4
EQUATION
OF
A LINE
10

Write answers in the
slope-intercept form
:
i)
Passes through (2,5) with the slope of ½
EXAMPLE
4
SOLUTION
11

Write answers in the
slope-intercept form
:
ii)
Passes through (1,-4) and (-5,4)
1)
EXAMPLE
4
SOLUTION
12

Write answers in the
slope-intercept form
:
iii) Perpendicular to the line 2x + y = 3 and
passes through (3,5)
EXAMPLE
4
EQUATION
OF
A LINE
13

iv) Parallel to the line 2x - 3y = 5 and passes
through (2,-1)
EXAMPLE
4
EQUATION
OF
A LINE
14

Example 5
Suppose an art object
purchased
for
$50,000
is
expected to
appreciate in value
at a
constant rate
of
$5000
per year for the next
5
years.

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- rita atake