mathematic f4 chapter 5 the straight line

1. Mf4 chapter 5
The straight line

2. 5.1 gradient of a straight line

4. Type of gradient

5. State the vertical distance, the horizontal
distance and the gradient of the line XY
Vertical distance
=
Horizontal
distance =
Gradient =

8. 5.2 gradient of straight lines in
cartesian coordinates.

9. Calculate the gradient of a straight line
passes through the two points as given.

10. Example 2

11. Example 3

12. Example 4

13. Example 5

14. Example 6

15. Based on the diagram below, state the straight
lines which have the gradient as given
(a)Positive gradient
:
(b)Negative
gradient :
(c)Zero gradient :
(d)Undefined
gradient :

16. 5.3 intercept
1. The x-intercept
is the x-
coordinate of
where the
straight line
cuts the x-axis
2. The y-intercept
is the y-
coordinate of
where the
straight line
cuts the y-axis.

17. gradient
Gradient , m = ̶ y-intercept
x-intercept
= ̶ b
a

18. 1. Determine the x-intercept, y-intercept
and gradient of the following straight line
X-intercept =
Y-intercept =
Gradient , m =

19. Example 2
Gradient , m =

20. Example 3
Gradient , m =

21. Example 4
Gradient , m =

22. 2. State the gradient of a straight line according
to the following x-intercept and y-intercept
(a) x-intercept = 4 (b) x-intercept = - 10
y-intercept = 6 y-intercept = 5
(c) x-intercept = 12 (d) x-intercept = - 3
y-intercept = - 4 y-intercept = -9

23. 3. State (i) x-intercept, (ii) y-intercept, (iii)
gradient of a straight line passes through the
points as given.
(a) (4, 0) and (0, 6)
(i) x-intercept =
(ii) y-intercept =
(iii)Gradient =

24. Example 2
(b) (0, 5) and ( - 10, 0)
(i) x-intercept =
(ii) y-intercept =
(iii)Gradient =

25. Example 3
(c) ( - 15, 0) and (0, 12 )
(i) x-intercept =
(ii) y-intercept =
(iii)Gradient =

26. Example 4
(d) ( 0, - 3) and ( - 5 , 0)
(i) x-intercept =
(ii) y-intercept =
(iii)Gradient =

27. 4. Find y-intercept of the following
(a) x- intercept = 4 (b) x-intercept = 3
gradient = ½ gradient = - 5/6

28. Find the x-intercept
(c) y-intercept = ½ (d) y-intercept = - 8
gradient = - ¾ gradient = 12

29. 5.4 equation of a straight line
1. The standard equation of a straight line is
y = mx + c
Where m = gradient
c = y-intercept

31. 1. Given the gradient, m and y-intercept, c.
Write the equation of the following straight line
(a) m = ̶ 3, c = 6 (b) m = 1/3 , c = ̶ 7

32. (c) m =2, c = 5 (d) m = - 2/5 , c = ̶ 3

33. Determine the gradient, m and y-
intercept, c, of the following equation.
(a) Y = 5x – 6 (b) y = ̶ x + 9
(c) 3y = 4x – 6 (d) 2 y = ̶ 8 x + 3

34. 3. Write the equation of y = mx + c
using given gradient and point.
(a) m = 2, ( - 3 , 0) (b) m = - 2/3 ; ( 0, 4)

35. (c) M = ¼; (5, ̶ 2 ) (d) m = ̶ 4/5, ( ̶ 10, 7)

36. 4. Write the equation when given two
points.
(a) (4,8), (2, 6)

37. (b) ( 3, 6) ,( ̶ 1, 7 ) (c) ( ̶ 2, ̶ 5) , (1 , 4)

38. (d) (2, ̶̶̶ 3) , ( ̶ 3 , ̶ 10)

39. 5. Find the equation of the following
straight lines.
(a) GH (b) IJ
(c) HI (d) GJ

40. 6. Find the intersection point of the straight lines by
drawing the lines .

42. 7. Find the intersection point by
solving the simultaneous equation .
(a) y = 5x + 6, y = 3x – 2

43. Example 2
(b) y = ̶ x + 4, 3 y = x – 12

44. Example 3
(c) y = 3x + 2, y = ̶ x + 5

45. Example 4
(d) 3x + 5y = 7, 7 x – 6y = ̶ 19

46. Example 5
(e) Y = ½ x + 8 , 5x + 3y = 11

47. 5.5 parallel lines
both lines are parallel , if
m₁ = m₂

48. 1. Determine whether the following
pair of straight line is parallel or not.
(a) y = x + 1
y + x = 7

49. Example 2
(b) y – 0.2 x = 2
5 y = x + 6

50. Example 3
(c) 2 y – x = 10
x = 5 – 2 y

51. Example 4
(d) x – 3y = 9
y – 1/3 x + 9 = 0

52. 2. Find the equation of a straight line passes through a
point and parallel to the straight line given.
example 1 :
y = 3 – 5x ; (4,5)

53. Example 2
y = 2 – 3x ; (3, ̶ 1 )

54. Example 3
x – 3y = 1 ; ( ̶ 3, 6)

55. Example 4
4y – 3x + 5 = 0 ; (3, ̶ 2)