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Class 9 Maths Part 2 Chapter 13 – Two Variables, One Line | Ganita Manjari Worksheet

Practise Class 9 Maths Part 2 Chapter 13 – Two Variables, One Line with this Ganita Manjari worksheet. Prepare more with important questions and revision exercises designed to strengthen understanding of linear relationships, improve mathematical practice and support effective preparation for class tests and examinations.

Class 9 Maths – Chapter 13: Two Variables, One Line

Fresh Worksheet – Extra Questions

Instructions: Solve all questions. Show necessary steps wherever required. Draw graphs neatly using a ruler.

Q1. Check whether the ordered pair (3, 2) is a solution of the equation 2x + 3y = 12.
Q2. Find any three solutions of the equation x + 2y = 8.
Q3. Find any four solutions of the equation 3x – y = 5.
Q4. Check whether the following points lie on the line 4x + y = 10:
  1. (1, 6)
  2. (2, 2)
  3. (0, 10)
Q5. Find the value of k if (2, 3) is a solution of the equation kx + 2y = 14.
Q6. Find the value of m if (4, -1) is a solution of mx + 3y = 17.
Q7. Write the equation represented by the following statement: “The sum of twice x and three times y is 18.”
Q8. Write the following equation in the form ax + by + c = 0: 5x = 2y + 7.
Q9. Write the equation represented by: “The difference between three times x and twice y is 9.”
Q10. Find the x-intercept and y-intercept of the line 2x + 3y = 12.
Q11. Find the x-intercept and y-intercept of the line 5x + 2y = 20.
Q12. Draw the graph of x + y = 6.
Q13. Draw the graph of 2x + y = 8.
Q14. Draw the graph of 3x – y = 6.
Q15. Plot the points (2, 3), (-2, 3), (-2, -3) and (2, -3) on a Cartesian plane. State the quadrant in which each point lies.
Q16. In which quadrant does each of the following points lie?
  1. (5, -2)
  2. (-4, 6)
  3. (-3, -7)
  4. (8, 4)
Q17. Give two points lying on the line y = 2x + 1.
Q18. Find two points lying on the line y = 5 – x.
Q19. Find the slope of the line passing through the points (1, 2) and (4, 8).
Q20. Find the slope of the line passing through (-2, 5) and (3, -5).
Q21. A line rises 12 units vertically when it moves 4 units horizontally. Find its slope.
Q22. A road falls 15 metres vertically for a horizontal distance of 60 metres. Find the slope of the road.
Q23. Find the slope of the line represented by y = 4x – 7.
Q24. Find the slope of the line represented by 2y = 6x + 8.
Q25. State whether the following lines have positive or negative slope:
  1. y = 3x + 2
  2. y = -4x + 5
  3. y = 7x – 1
  4. y = -2x – 6
Q26. Find the value of y when x = 4 in the equation 3x + 2y = 18.
Q27. Find the value of x when y = -2 in the equation 5x – 2y = 14.
Q28. Find three points on the line 2x – 3y = 6.
Q29. Determine whether the point (5, 4) lies on the line 2x + y = 14.
Q30. Determine whether the point (-3, 5) lies on the line x – 2y = -13.
Q31. The cost of one notebook is x rupees and the cost of one pen is y rupees. If 3 notebooks and 2 pens cost Rs. 110, form a linear equation in x and y.
Q32. The perimeter of a rectangle is 40 cm. If its length is x cm and breadth is y cm, form a linear equation connecting x and y.
Q33. A taxi charges a fixed amount of Rs. 50 and Rs. 12 per kilometre. If the total fare is y rupees for x kilometres, form a linear equation connecting x and y.
Q34. Find the equation of the line passing through the points (0, 5) and (5, 0).
Q35. Find the equation of the line whose x-intercept is 6 and y-intercept is 3.
Q36. If the line ax + 3y = 12 passes through the point (3, 1), find the value of a.
Q37. If (2, -3) is a solution of 4x + ky = 5, find k.
Q38. Find two different points on the line 4x + 2y = 12.
Q39. A line passes through (2, 4) and (6, 12). Find its slope. Also state whether the line rises or falls from left to right.
Q40. A line passes through (-1, 5) and (3, -3). Find its slope.
Q41. Complete the table for the equation 2x + y = 10.
x0245
y
Q42. Complete the table for x – 2y = 6.
x02610
y
Q43. The points (1, 3), (2, 5) and (3, 7) are given. Check whether all three points lie on the same line.
Q44. The points A(1, 2), B(3, 6) and C(5, 10) are given. Find the slope of AB and BC. What do you observe?
Q45. Explain why the graph of a linear equation in two variables is a straight line.
Q46. Can a linear equation in two variables have more than two solutions? Explain with an example.
Q47. Can the graph of a linear equation in two variables pass through the origin? Give an example.
Q48. Find the point where the line 3x + 2y = 12 meets the y-axis.
Q49. Find the point where the line 4x – y = 8 meets the x-axis.
Q50. Draw the graph of 2x + 3y = 6. From the graph, identify its x-intercept and y-intercept.

Answer Sheet

  1. Yes.
  2. For example: (0,4), (2,3), (4,2).
  3. For example: (0,-5), (1,-2), (2,1), (3,4).
  4. (1,6) lies on the line; (2,2) lies on the line; (0,10) lies on the line.
  5. k = 4.
  6. m = 5.
  7. 2x + 3y = 18.
  8. 5x – 2y – 7 = 0.
  9. 3x – 2y = 9.
  10. x-intercept = 6, y-intercept = 4.
  11. x-intercept = 4, y-intercept = 10.
  12. Any two or more points satisfying x + y = 6, such as (0,6), (2,4), (6,0).
  13. Any two or more points satisfying 2x + y = 8, such as (0,8), (2,4), (4,0).
  14. Any two or more points satisfying 3x – y = 6, such as (0,-6), (2,0), (4,6).
  15. (2,3) – I; (-2,3) – II; (-2,-3) – III; (2,-3) – IV.
  16. (5,-2) – IV; (-4,6) – II; (-3,-7) – III; (8,4) – I.
  17. For example: (0,1), (1,3).
  18. For example: (0,5), (5,0).
  19. 2.
  20. -2.
  21. 3.
  22. -1/4.
  23. 4.
  24. 3.
  25. Positive, negative, positive, negative.
  26. y = 3.
  27. x = 2.
  28. For example: (0,-2), (3,0), (6,2).
  29. Yes.
  30. Yes.
  31. 3x + 2y = 110.
  32. 2x + 2y = 40, or x + y = 20.
  33. y = 12x + 50.
  34. x + y = 5.
  35. x + 2y = 6.
  36. a = 3.
  37. k = 1.
  38. For example: (0,6), (3,0).
  39. Slope = 2; the line rises from left to right.
  40. Slope = -2.
  41. y-values: 10, 6, 2, 0.
  42. y-values: -3, -2, 0, 2.
  43. Yes, the three points are collinear.
  44. Both slopes are 2; the points lie on the same straight line.
  45. Because the variables have degree one, their values form a straight-line relationship when plotted.
  46. Yes. A linear equation in two variables generally has infinitely many solutions.
  47. Yes. Example: x + y = 0.
  48. (0,6).
  49. (2,0).
  50. x-intercept = 3, y-intercept = 2.

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