Find the equation of straight line L 1 4 1. (a) (b) y x O the equation of straight line L in each of the following. (1 − 4) y1. (a) (b) y2. (a) (b) 3. (a) (b) 4. (a) (b) 5. If straight

Find the equation of straight line L in each of the following. (1 − 4)

1. (a) (b)

2. (a) (b)

3. (a) (b)

4. (a) (b)

5. If straight line 0253: =−+ kyxL passes through the origin, find the value of k.

6. If straight line 063: =+− kyxL passes through )6 ,4( −P , find the value of k.

y

Ox

L

1 Slope = 12

y

Ox

L

Slope = −1−1

8

y

Ox

L

6

y

Ox

−2

2

L

y

Ox

L4

y

Ox

L(−3, −3) (3, −3)

y

Ox

L

10

y

Ox

L(−2, 7)

(−2, 1)

7. If straight line 0634: =+− yxL passes through ) ,0( pP , find the coordinates of P.

8. In each of the following, find the equation of the straight line with the slope of m passing through A.

(a) 1 ,)2 ,3( =−− mA

(b) 2 ,)2 ,2( −=mA

(c) 31 ,)0 ,5( =mA

9. In each of the following, find the equation of the straight line passing through A and B.

(a) )4 ,0( ,)8 ,6( BA −−

(b) )7 ,2( ,)5 ,3( −−− BA

(c) )52 ,

21( ,)

101 ,

43( BA −

10. Find the equation of the straight line with each set of the conditions given. (a) Passing through )4 ,2( −P , y-intercept = −2

(b) Passing through )6 ,3( P , x-intercept = 9

(c) Passing through )31 ,

31( −−P , x-intercept = 1

11. It is given that straight line L with the slope of −3 passes through )1 ,6( A and ) ,4( bB .

(a) Find the equation of L.

(b) Find the value of b.

12. It is given that the x-intercept and y-intercept of straight line L are 1 and 2 respectively.

(a) Find the equation of L.

(b) Does )21 ,

43( A lie on L?

13. In the figure, straight lines kxyL += 2:1 and 2L intersect at )3 ,1( kP .

(a) Find the value of k. (b) If the x-intercept of 2L is 5, find the equation of 2L .

5

y

Ox

L2

P (1, 3k)

L1 : y = 2x + k

14. (a) If straight line )3(21: −= xyL passes through ) ,13( kkP + , find the coordinates

of P.

(b) Find the equation of the straight line with the slope of 1 passing through P.

15. In the figure, straight lines 1L and 2L intersect at )12 ,2( −kkP . It is given that the slope of 2L is 2.

(a) Find the coordinates of P. (b) Find the equation of 2L .

16. In the figure, vertical line 1L , horizontal line 2L and straight line 3L pass through A. 3L passes through the origin.

(a) Write down the coordinates of A. (b) Find the equation of 3L .

17. In the figure, straight line 1L passes through )3 ,3( P , Q and the origin. Straight line 2L passes through Q and )5 ,0( −R .

(a) Find the equation of 1L .

(b) Find the equation of 2L .

(c) Find the coordinates of Q.

18. In the figure, straight lines 02:1 =−+ byxL

and 3:2 =xL intersect at ) ,( baA .

(a) Find the coordinates of A. (b) Find the equation of the straight line

passing through the origin and A.

y

Ox

L2 : x = 3

A (a, b)

L1 : x + y − 2b = 0

y

Ox

L1

L2

P (3, 3)

R (0, −5)Q

y

Ox

L1 : x = 4

L2 : y = 6A

L3

y

Ox

L2

P (2k, 2k − 1)

L1 : y = − x − 412

19. It is given that straight line L passes through )5 ,1( −A . If the x-intercept of L is twice its y-intercept, find the equation of L.

20. In the figure, straight lines 1L and 2L pass through )2 ,( +aaA . Straight line 2L intersects the y-axis at B and OBOA = .

(a) Find the coordinates of A and B. (b) Find the equation of 2L .

21. In the figure, straight line L cuts the x-axis and y-axis at A and B respectively. )3 ,2( −M is the

mid-point of AB.

(a) Find the x-intercept and y-intercept of L. (b) Find the equation of L.

22. It is given that three points )6 ,8( −A , ) ,0( bB and )15 ,4( C are collinear.

(a) Find the value of b. (b) If straight line L passes through B and its x-intercept is 15, find the equation of

L.

23. Two points A(−5, 4) and B(−2, −2) are given. C is a point on AB produced such

that 2:3: =BCAB .

(a) Find the coordinates of C. (b) Find the equation of the straight line with the slope of 2 passing through C.

24. Two points A(0, 8) and B(−4, 0) are given. If C is a point on the x-axis such that the area of ΔABC is 16 square units and C is on the left hand side of B,

(a) find the coordinates of C. (b) find the equation of AC.

y

Ox

L2

A (a, a + 2)

L1 : 4x − 3y = 0

B

A Ox

y

L

B

M (−2, 3)

C Ox

y

A (0, 8)

B (−4, 0)

25. Convert the following equations of straight lines into the general form.

(a) 632

+= xy (b) 121 3

2 =−

+yx (c) )1(

41

−−= xy

26. Find the x-intercept, y-intercept and slope of the straight line represented by each of the following equations.

(a) 08 =+− yx (b) 27 −= yx (c) )13(31

+= xy

27. If the slope of straight line 03)1(: =++ yxkL is 2, find the value of k.

28. If the y-intercept of straight line 0243: =++− kyxL is −2, find the value of k.

29. If the x-intercept of straight line 0132: =−−+ kykxL is −1, find the value of k.

30. It is given that L is a straight line with the slope of

52

and the y-intercept of 1.

(a) Find the equation of L. (b) Find the x-intercept of L.

31. It is given that L is a straight line with the slope of −4 and the x-intercept of

21

− .

(a) Find the equation of L. (b) Find the y-intercept of L.

32. It is given that L is a straight line with the slope of

34

passing through )1 ,6( A .

(a) Find the equation of L. (b) Find the x-intercept and y-intercept of L. 33. It is given that )3 ,3( A and )5 ,1( −B are two points on straight line L.

(a) Find the equation of L. (b) Find the x-intercept and y-intercept of L. 34. It is given that the x-intercept of straight line 0)1(2:1 =+−− kykxL is 3.

(a) Find the value of k. (b) Find the slope and y-intercept of L. 35. It is given that the slope of straight line 09: =−+ ykxL is −2.

(a) Find the value of k. (b) Find the x-intercept of L. (c) Does )3 ,3( A lie on L?

36. It is given that the y-intercept of straight line 010)3()2(: =−−+− ykxkL is 5.

(a) Find the value of k. (b) Find the x-intercept and slope of L. (c) Does L pass through )7 ,1( A ?

37. It is given that the x-intercept and y-intercept of straight line 012)4()12(: =++−− ykxkL are equal.

(a) Find the value of k. (b) Find the equation of L. (c) Find the slope of L.

38. It is given that L is a straight line with the x-intercept of −3m and the y-intercept of 2m where m ≠ 0.

(a) Express the equation of L in terms of m.

(b) If the slope of L is

m6

− , find the value of m.

(c) Prove that A(3m, 4m) lies on L.

39. It is given that straight line 01223:1 =−+ yxL cuts the x-axis and y-axis at P and Q respectively. M is the mid-point of P and Q.

(a) Find the coordinates of P, Q and M. (b) If straight line 2L passes through M and its slope is

31 ,

(i) find the equation of 2L . (ii) find the x-intercept and y-intercept of 2L .

40. It is given that straight line 04)32(: =+−+ ykkxL passes through )8 ,2( −P and cuts the x-axis and y-axis at A and B respectively.

(a) Find the value of k. (b) Find the area of OABΔ .

41. In the figure, straight line 2L passes through )1 ,1( −A and intersects straight line 0632:1 =−+ yxL at the x-axis.

(a) Find the equation of 2L .

(b) Find the y-intercept of 2L .

(c) Find the area of the shaded region.

y

Ox

A (−1, 1)

L1 : 2x + 3y − 6 = 0

L2

42. In the figure, straight lines 0105:1 =+− ykxL and

0)43(3:2 =−−+ kkyxL cut the y-axis at A. 1L and 2L cut the x-axis at B and C respectively.

(a) Find the coordinates of A.

(b) Find the value of k. (c) Find the ratio of the area of OABΔ to that of OACΔ .

43. In the figure, straight line 03634:1 =++ yxL cuts the x-axis and y-axis at A and B respectively. C is a point on 1L such that 1:2: =CBAC . M is the mid-point of O and B.

(a) Find the coordinates of C and M. (b) If straight line 2L passes through C and M,

(i) find the equation of 2L . (ii) find the x-intercept of 2L .

44. It is given that the slope of straight line 015)2(: =++− ykkxL is 3.

(a) Find the value of k.

(b) If L cuts the x-axis and y-axis at P and Q respectively, which point, P or Q, is closer to the origin? Explain briefly.

y

Ox

A

L1 : kx − 5y + 10 = 0

B CL2 : 3x + ky − (3k − 4) = 0

L1 : 4x + 3y + 36 = 0

O

C

A

M

B

y

x

L2