Mathematics Title: Equations of Straight Line O y x

Mathematics

Title: Equations of Straight Line

O

y

x

Student Name: Ma Lai Har

Student I.D. No.: 98041880

Course Code: EDD 5161F

Lecturer: Dr. Lee Fong Lok

Dr. Leung Chi Hong

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..

Standard Forms of A Straight Line

A. Two-Point Form

B. Point-Slope Form

C. Slope-Intercept Form

D. Intercept Form

E. General Form

x 22 , yxBy

Ox

x

11, yxA

x yxP ,

Two-Point Form

Given a straight line which passes through the points A and B, then

12

12

xx

yy

Slope of AB =

If P(x, y) is any point on the line AB, then

1

1

xx

yy

Slope of PA =

Since PA and AB are parts of the same straight line, then

Slope of PA = Slope of AB

12

12

xx

yy

1

1

xx

yy

=

This equation is known as the Two-Point Form of the straight line. (Go to Example 1)

i.e.


A. Two-Point Form

B. Point-Slope Form


D. Intercept Form

E. General Form

Point-Slope Form

x

y

Ox

11, yxA

x

yxP ,Slope = m

Given a straight line which passes through the point A and has m as its slope.

If P(x, y) is any point on the line , then

1

1

xx

yy

Slope of PA =

Since slope of PA equals to the slope of the straight line, then

1

1

xx

yy

= m

11 xxmyy i.e.

This equation is known as the Point-Slope Form of the straight line. (Go to Example 2)


A. Two-Point Form

B. Point-Slope Form


D. Intercept Form

E. General Form

O

y

x

c

A(0, c)x

xP(x, y)

Slope = m

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.)

If P is any point on the line, then

Slope of PA = 0

x

cy

Since slope of PA is equal to the slope of the line, then by Point-Slope Form

(y - c) = m(x – 0)

y = mx + ci.e.

This equation is known as the Slope-Intercept Form of the straight line. (Go to Example 3)


A. Two-Point Form

B. Point-Slope Form


D. Intercept Form

E. General Form

Intercept Form

x

xa

b

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.)

x

y

Ox

B(0, b)

A(a, 0)

P(x, y)

=

a

b

0

0Slope of AB =

a

b

ax

y

0

Slope of PA =

If P is any point on the line, then

Since the slope of PA equals to the slope of AB, then

ax

y

0

a

b=

bx + ay = abDividing both sides by ab, we have

1b

y

a

x

This equation is known as the Intercept Form of the straight line. (Go to Example 4)


A. Two-Point Form

B. Point-Slope Form


D. Intercept Form

E. General Form

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.


A. Two-Point Form

B. Point-Slope Form


D. Intercept Form

E. General Form

Mathematics

Title: Equations of Straight Line

O

y

x

Example 1 (Two-Point Form)

y

Ox

x

x yxP ,

x

A(1, 3)

B(5, 6)Find the equation of the straight line.

The required equation:

15

36

1x

3y

4(y – 3) = 3(x – 1)

i.e. 3x – 4y + 9 = 0

(Note: The answer is in General Form)

Example 2 (Point-Slope Form)

y

Ox

Slope = 2 P(x, y)x

A(1, 3)x

Find the equation of the straight line.


y – 3 = 2(x – 1)

i.e. 2x – y + 1 = 0


Example 3 (Slope-Intercept Form)

xA(0, 4)

Slope = 2



y = 2x + 4

i.e. 2x – y + 4 = 0


y

xO

xP(x, y)

Example 4 (Intercept Form)

y

Ox

B(0, 5)

A(7, 0)

P(x, y)

x

x

x



15

y

7

x

5x + 7y = 35

i.e. 5x + 7y – 35 = 0


Documents

Mathematics Title: Equations of Straight Line O y x