1. CHAPTER 5 The Straight Line

2. Learning Objectives
5.1 Understand the concept of gradient of a straight line.
5.2 Understand the concept of gradient of a straight line in Cartesian coordinates.
5.3 Understand the concept of intercept.
5.4 Understand and use equation of a straight line.
5.5 Understand and use the concept of parallel lines.

3. Equation of straight line
The Straight Line
Gradient
Intercept
y-intercept
x-intercept
Equation of straight line
Gradient = m
y-intercept = c
Parellel lines

4. 5.1 GRADIENT OF A STRAIGHT LINE
(A) Determine the vertical and horizontal distances between two given points on a straight line F E G
Example of application: AN ESCALATOR.
EG - horizontal distance(how far a person goes)
GF - vertical distances(height changed)

5. Example 1
State the horizontal and vertical distances for the following case.
10 m
16 m
Solution:
The horizontal distance = 16 m
The vertical distance = 10 m

6. (B)Determine the ratio of the vertical distance to the horizontal distance
Let us look at the ratio of the vertical distance to the horizontal distances of the slope as shown in figure.

7. Therefore, Solution: Vertical distance = 10 m
Horizontal distance = 16 m
Therefore,
Solution:

8. 5.2 GRADIENT OF THE STRAIGHT LINE IN CARTESIAN COORDINATES
Coordinate T = (X2,Y1)
horizontal distance
= PT
= Difference in x-coordinates
= x2 – x1
Vertical distance
= RT
= Difference in y-coordinates
= y2 – y1 y
R(x2,y2)
y2 – y1
x2 – x1
T(x2,y1)
P(x1,y1) x

9. Solution:
REMEMBER!!!
For a line passing through two points (x1,y1) and (x2,y2),
where m is the gradient of a straight line

10. Example 2
Determine the gradient of the straight line passing through the following pairs of points
P(0,7) , Q(6,10)
L(6,1) , N(9,7)
Solution:

11. (C) Determine the relationship between the value of the gradient and the
Steepness
Direction of inclination of a straight line
What does gradient represents??
Steepness of a line with respect to the x-axis.

12. B
a right-angled triangle. Line AB is a slope, making an angle with the horizontal line AC A C

13. When gradient of AB is positive: When gradient of AB is negative:y y B B x x A A
inclined upwards
acute angle
is positive
inclined downwards
obtuse angle.
is negative

14. Activity: Determine the gradient of the given lines in figure and measure the angle between the line and the x-axis (measured in anti-clocwise direction) y
Line
Gradient
Sign MN PQ RS UV
V(1,4)
N(3,3)
Q(-2,4)
S(-3,1) x
M(-2,-2)
R(3,-1)
P(2,-4)
U(-1,-4)

15. REMEMBER!!! The value of the gradient of a line:
Increases as the steepness increases
Is positive if it makes an acute angle
Is negative if it makes an obtuse angle

16. Lines
Gradient AB y A B x

17. Lines
Gradient CD
Undefined y D C x

18. Lines
Gradient EF
Positive y F E x

19. Lines
Gradient GH
Negative y H G x

20. AB CD EF GH Undefined Positive Negative Lines Gradient y D H F A B G ECD
Undefined EF
Positive GH
Negative y D H F A B G E C x

21. 5.3 Intercepts Another way finding m, the gradient: y-intercept
x-intercept
Another way finding m, the gradient:

22. 5.4 Equation of a straight line
Slope intercept form
y = mx + c
Point-slope form
given 1 point and gradient:
given 2 point:

23. 5.5 Parallel lines
When the gradient of two straight lines are equal, it can be concluded that the two straight lines are parallel.
Example:
Is the line 2x-y=6 parallel to line 2y=4x+3?
Solution:
2x-y=6y y=2x gradient is 2.
2y=4x gradient is 2.
Since their gradient is same hence they are parallel.