Math(f4)-straight Line 5.1

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MATHEMATICS FORM 4

5

CHAPTE R

THE STRAIGHT LINE

LEARNING OUTCOMES By the end of the lesson, student should be able to: (a)Determine the vertical and horizontal distances between two given points on a straight line. (b)Determine the gradient of a straight lines using ratio of vertical distance to horizontal distance. (c) Form formula of gradient of straight line (d) Calculate the gradient of a straight line passing through two points.

5.1

THE GRADIENT OF A STRAIGHT LINE

B VERTICAL DISTANCE

A

C HORIZONTAL DISTANCE

What is a gradient of a straight line ? Gradient of a straight line is the ratio of the vertical distance to horizontal distance.

Gradient of a straight line =

Vertical Distance Horizontal Distance

B VERTICAL DISTANCE

A

C HORIZONTAL DISTANCE

Gradient of AB =

Vertical Distance = CB Horizontal Distance AC

EXAMPLE 1 (i) Identify the vertical distance and horizontal distance between point A and B. (ii) Find the gradient of a straight line AB.

1 (a)

B

VERTICAL DISTANCE = HORIZONTAL DISTANCE =

GRADIENT OF AB =

A

5m

7m

C

1 (a)

vertical distance

B

VERTICAL DISTANCE =

5

HORIZONTAL DISTANCE =

GRADIENT OF AB =

A

5m

7m

C

1 (a)

B

VERTICAL DISTANCE =

5

HORIZONTAL DISTANCE =

5m

7

GRADIENT OF AB =

5 7

A

7m horizontal distance

C

1 (b)

B

VERTICAL DISTANCE = HORIZONTAL DISTANCE = GRADIENT OF AB =

A

C

1 (b)

B

VERTICAL DISTANCE = 4

+1 UNITS

units

+1 VERTICAL UNITS

HORIZONTAL DISTANCE = GRADIENT OF AB =

DISTANCE

A

C

+1 UNITS +1 UNITS

1 (b)

B

VERTICAL DISTANCE = 4

units

HORIZONTAL DISTANCE = 5

units GRADIENT OF AB =

4 5

A

+1 UNITS

+1 UNITS

C HORIZONTA L +1 +1 +1 DISTANCE UNITS UNITS UNITS

WORKSHEET 1 (4 minutes)

5.2

GRADIENT OF THE STRAIGHT LINE IN CHARTESIAN COORDINATES

y

(x,y)

origin (0,0)

x

y

3

(3 units) (3,2)

2

(2 units)

1 -4

-3

-2

-1

1 -1 -2 -3

2

3

4

x

y A (1,3)

3

B (-2,2) 2 1 -4

-3

-2

-1

1 -1 -2 -3

2

3

4

x

y

B vertical distance

A horizontal distance X

Gradient, m of a straight line passing through points A and B is given by;

EXAMPLE 2 Calculate the gradient of straight line in the following figure.

GRADIENT OF LINE PQ Q ( 4,4 )

P ( 1,0 )

=

Q ( 4,4 )

P ( 1,0 ) Let Then, ,

and ,

Let Then, and

OR Gradient of line PQ;

and ,

,

Gradient of line PQ;

and

GRADIENT OF LINE PQ Q ( 4,4 )

P ( 1,0 )

=

4 3

WORKSHEET 2 (5 minutes)

POP QUIZ…

Given that the gradient of a straight line passing through points P(2,5) and Q(h,9) is 2. Find the value of h. A

6

B

-3

C

4

D

5

YOUR ANSWER IS WRONG √ -PLEASE TRY AGAIN-

BAC K

CONGRATULATION YOUR ANSWER IS CORRECT

NEX T

SUMMARY Gradient of a straight line =

Vertical Distance Horizontal Distance y

In Cartesian coordinate; vertical distance

Gradient, m= OR

m=

horizontal distance X

THANK YOU...