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LINEAR LAW SPM questions involved this chapter are tested in : 1. Paper 1 (3 or 4 marks) 2. Paper 2 (Part B, 10 marks) A. General Form of Linear Relations ã Any non-linear relations can be reduced to linear relations in the form of: Y = mX + c. Horizontal axis Only represented by variable/s and multiply with the constant that is represented by gradient. Vertical axis Only represented by variable/s Vertical axis intercept Only formed by constant .
Y = mX+c
Gradient constant Only formed by consta

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LINEAR LAW
SPM questions involved this chapter are tested in :1.Paper 1 (3 or 4 marks)2.Paper 2 (Part B, 10 marks)
A. General Form of Linear Relations
ã
Any non-linear relations can be reduced to linear relations in the form of:
Y
=
mX
+
c.
ã
The method of reducing to linear relation depends on the srcinal relation (non-linear) given.
ã
It is vital to determine what form of variables and constants in a relation.
ã
When the variables and constant are determined, the process of reducing non-linear to linear will form a general linear equation,
Y
=
mX
+
c.
ã
The value of the
x
-variable and the
y
-variable must follow the corresponding horizontal axisand the vertical axis of the linear form of the equation.
B. Method of conversion
The method used depend on the non-linear relation that is given. In general, three (3) methods apply:i.use of log;ii.operation of algebra i.e. multiplication or division; andiii. squaring of equation
i. Application of Log
The use of log is needed in reducing relation if there is form of algebraic or instance of indices . For example; SPM2000.P1.Q16
y
=
ab
x
−
1
where
x
and
y
are variables and
a
and
b
are constants.
Horizontal axis
Only represented by variable/sand multiply with the constantthat is represented by gradient.
Vertical axis
Only represented byvariable/s
Gradient constant
Only formed by constantand rely on or multiply tothe variable of horizontalaxis.
Vertical axis intercept
Only formed by constant .
Y
=
m X
+
c
log y
=
log
ab
x
−
1
log y
=
log a
+
log b
x
−
1
log y
=
log a
+
(x-1) log blog y =
log b(x-1)
+
log ay = m x + c
Therefore
y
is the vertical axis,
x-1
is the horizontal axis,
log b
is the gradient and
log a
is theintercept.
ii. Operation of Algebra
The use of algebraic operation usually involves non-linear relation in a quadratic function form. For example; SPM2001.Q1.Q16
S = ut
+
at
2
S
and
t
are variables and
u
and
a
are constants.Divide
t
on both sides of the equation:
S t
=
ut t
at
2
t
S t
=
u
at S t
=
at
u
y = mx + c
Hence,
S t
is the vertical axis
, a
is the gradient
, t
is the horizontal axis and
u
is the intercept.
iii. Squaring of Equation
The use of square is used when a relation has a (square) root form i.e.
.
. For example;SPM1995.P1.Q15
T
= 2
π
M k
where
T
and
M
are variables and
k
is a constant.Squaring both sides of the equation result in:
T
2
=
2
M k
2
T
2
=
4
2
M k
T
2
=
4
2
k M
y
=
mx
+
cT
2
is the vertical axis,4
2
k
is the gradient,
M
is the horizontal axis and the gradient is zero.

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