Mathematics

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Mathematics
Title Equations of Straight Line
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Student Name Ma Lai Har
Student I.D. No. 98041880
Course Code EDD 5161F
Lecturer Dr. Lee Fong Lok Dr. Leung Chi
Hong
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Introduction
The target audience of this package is Form Three
Students whose level is intermediate (Band 3).
The package is used in the classroom for
lecturing or self-learning. After the simple
introduction of each form of equation of straight
line, an example is given. Therefore, students
can have a deeper understanding with the topic..
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Standard Forms of A Straight Line A. Two-Point
Form B. Point-Slope Form C. Slope-Intercept
Form D. Intercept Form E. General Form
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Two-Point Form
y
x
Given a straight line which passes through the
points A and B, then
x
x
If P(x, y) is any point on the line AB, then
x
O
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Since PA and AB are parts of the same straight
line, then
Slope of PA Slope of AB
i.e.
This equation is known as the Two-Point Form of
the straight line.
(Go to Example 1)
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Standard Forms of A Straight Line A. Two-Point
Form B. Point-Slope Form C. Slope-Intercept
Form D. Intercept Form E. General Form
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Point-Slope Form
Given a straight line which passes through the
point A and has m as its slope.
x
Slope m
If P(x, y) is any point on the line , then
x
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Since slope of PA equals to the slope of the
straight line, then
i.e.
This equation is known as the Point-Slope Form of
the straight line.
(Go to Example 2)
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Standard Forms of A Straight Line A. Two-Point
Form B. Point-Slope Form C. Slope-Intercept
Form D. Intercept Form E. General Form
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Slope-Intercept Form
Given a straight line which cuts the y-axis at A
and with slope m . (Note c is called the
y-intercept of the straight line.)
x
P(x, y)
A(0, c)
x
c
If P is any point on the line, then
Slope m
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Since slope of PA is equal to the slope of the
line, then by Point-Slope Form
(y - c) m(x 0)
y mx c
i.e.
This equation is known as the Slope-Intercept
Form of the straight line.
(Go to Example 3)
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Standard Forms of A Straight Line A. Two-Point
Form B. Point-Slope Form C. Slope-Intercept
Form D. Intercept Form E. General Form
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Intercept Form
Given a straight line which cuts the x-axis at A
and y-axis at B. (Note a is called the
x-intercept of the straight line.)
B(0, b)
x
P(x, y)
b
x
A(a, 0)
x
a
If P is any point on the line, then
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Since the slope of PA equals to the slope of AB,
then
bx ay ab
Dividing both sides by ab, we have
This equation is known as the Intercept Form of
the straight line.
(Go to Example 4)
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Standard Forms of A Straight Line A. Two-Point
Form B. Point-Slope Form C. Slope-Intercept
Form D. Intercept Form E. General Form
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General Form
It should be noted that all the different
standard forms of the equation of a straight line
can be reduced to the form
Ax By C 0
where A, B and C are constants with A and B not
both zero.
This equation is known as the General Form of a
straight line.
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Standard Forms of A Straight Line A. Two-Point
Form B. Point-Slope Form C. Slope-Intercept
Form D. Intercept Form E. General Form
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THE END
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Mathematics
Title Equations of Straight Line
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Example 1 (Two-Point Form)
Find the equation of the straight line.
B(5, 6)
x
The required equation
x
x
A(1, 3)
4(y 3) 3(x 1)
i.e. 3x 4y 9 0
(Note The answer is in General Form)
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Example 2 (Point-Slope Form)
Find the equation of the straight line.
x
Slope 2
P(x, y)
The required equation
y 3 2(x 1)
x
A(1, 3)
i.e. 2x y 1 0
(Note The answer is in General Form)
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Example 3 (Slope-Intercept Form)
Find the equation of the straight line.
P(x, y)
x
The required equation
A(0, 4)
x
y 2x 4
i.e. 2x y 4 0
Slope 2
(Note The answer is in General Form)
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Example 4 (Intercept Form)
Find the equation of the straight line.
The required equation
B(0, 5)
x
P(x, y)
x
5x 7y 35
A(7, 0)
x
i.e. 5x 7y 35 0
(Note The answer is in General Form)