Intersection and angles between lines - One Line Questions

1. Two lines are perpendicular. If the slope of one line is 3, what is the slope of the other line? — -1/3
2. If the lines 3x - 2y + 5 = 0 and kx + 4y - 1 = 0 are parallel, find the value of k. — -6
3. Find the point of intersection of the lines 4x + 3y = 1 and x - y = 2. — (1, -1/3)
4. Find the point of intersection of the lines x + 2y = 1 and 3x + 4y = -1. — (-3, 2)
5. Find the point of intersection of the lines x - y = 0 and x + y = 0. — (0, 0)
6. Find the point of intersection of the lines x + y - 1 = 0 and x - y + 1 = 0. — (0, 1)
7. What is the point of intersection of the lines 2x + 3y - 5 = 0 and 3x - 4y + 1 = 0? — (11/17, 23/17)
8. Find the point of intersection of the lines x - 2y = 5 and 2x + 3y = 1. — (17/7, -4/7)
9. Find the point of intersection of the lines 2x + y = 5 and x + y = 3. — (2, 1)
10. Find the point of intersection of the lines represented by the equations: x + y = 5 and 2x - y = 4. — (3, 2)
11. Find the point of intersection of the lines 3x + 2y = 7 and x - y = 1. — (3, 2)
12. Find the point of intersection of the lines x = 5 and y = 3. — (5, 3)
13. Find the angle between the lines x + 2y + 1 = 0 and 2x - y + 3 = 0. — 90 degrees
14. Find the acute angle between the lines x - y + 1 = 0 and x + y - 2 = 0. — 45 degrees
15. What is the angle between the lines 3x - 4y = 5 and 4x + 3y = 7? — 90 degrees
16. Find the angle between the lines y = mx and y = -x/m. — 90 degrees
17. Find the angle between the lines x cos(alpha) + y sin(alpha) = p and x sin(alpha) - y cos(alpha) = q. — 90 degrees
18. Find the angle between the lines y = x and y = -x. — 90 degrees
19. What is the angle between the lines x + sqrt(3)y = 1 and sqrt(3)x + y = 2? — 0 degrees
20. Find the angle between the line y = 2x + 3 and y = -x/2 + 1. — 90 degrees
21. Find the angle between the lines x + y = 1 and x - y = 1. — 90 degrees
22. Find the angle between the lines 2x + 3y = 5 and 3x - 2y = 7. — 90 degrees
23. If the lines 2x + y - 3 = 0 and kx - 2y + 1 = 0 are perpendicular, find k. — 1
24. Find the value of k if the lines 3x + 4y - 1 = 0 and 6x + 8y - 3 = 0 are parallel. — 2
25. The lines 5x + 2y - 7 = 0 and 4x + ky + 3 = 0 are perpendicular. Find the value of k. — 10/4
26. Find the angle between the line y = (2 - sqrt(3))x + 5 and y = (2 + sqrt(3))x - 7. — 60 degrees
27. Find the acute angle between the lines y = (sqrt(3) - 1)x and y = (sqrt(3) + 1)x. — 60 degrees
28. If the lines 2x - 3y + 1 = 0 and kx + 6y - 5 = 0 are parallel, find k. — -4
29. Find the value of k if the lines 5x - 3y + 2 = 0 and 10x - 6y + k = 0 are coincident. — 4
30. Find the value of k such that the lines 2x + 3y - 1 = 0 and 4x + ky + 5 = 0 are parallel. — 6
31. If the lines 3x + 2y - 1 = 0 and kx - 4y + 5 = 0 are perpendicular, find k. — 6
32. If the lines 5x - 2y + 1 = 0 and kx + 4y - 3 = 0 are perpendicular, find k. — 8
33. What is the condition for the lines ax + by + c = 0 and dx + ey + f = 0 to be coincident? — a/d = b/e = c/f
34. If the lines x/a + y/b = 1 and x/c + y/d = 1 are parallel, then: — ad = bc
35. The lines ax + by + c = 0 and dx + ey + f = 0 are perpendicular if: — ae + bd = 0
36. If the lines ax + by + c = 0 and dx + ey + f = 0 are perpendicular, then: — ae + bd = 0
37. What is the condition for the lines ax + by + c = 0 and dx + ey + f = 0 to be parallel? — ae = bd
38. The lines ax + by + c = 0 and dx + ey + f = 0 are parallel if: — ae = bd
39. What is the angle between the line 2x - y + 5 = 0 and the x-axis? — arctan(2)
40. The angle between the lines ax + by + c = 0 and dx + ey + f = 0 is given by: — cos(theta) = |(ae + bd) / (sqrt(a^2 + b^2) * sqrt(d^2 + e^2))|
41. The lines x + 2y = 3 and 2x + 4y = 5 are: — Parallel
42. The lines x + 2y + 3 = 0 and 2x + 4y + 5 = 0 are: — Parallel
43. The lines x + y = 1 and 2x + 2y = 3 are: — Parallel
44. The lines x/3 + y/4 = 1 and x/6 + y/8 = 1 are: — Coincident
45. The lines x = 5 and y = x are: — Intersecting
46. If the lines y = m1x + c1 and y = m2x + c2 are parallel, then: — m1 = m2
47. If the lines y = m1x + c1 and y = m2x + c2 are perpendicular, then: — m1m2 = -1
48. The angle between the lines ax + by + c = 0 and x-axis is given by: — tan(theta) = -b/a
49. The angle between the lines y = m1x + c1 and y = m2x + c2 is given by: — tan(theta) = |(m1 - m2) / (1 + m1m2)|
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