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Class 10 > Learn Linear equations in 2 variables > 5. From the following graph, find four solutions of...
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5. From the following graph, find four solutions of the equation representing the line AB.

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Finding Solutions of Line AB Equation Given Information: Line AB is represented by the equation. A graph depicting Line AB is provided. Procedure: Identify Points on Line AB: Locate four points on the graph that lie on Line AB. Determine Coordinates: Extract the coordinates of these points. Substitute...
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Finding Solutions of Line AB Equation

Given Information:

  • Line AB is represented by the equation.
  • A graph depicting Line AB is provided.

Procedure:

  1. Identify Points on Line AB: Locate four points on the graph that lie on Line AB.
  2. Determine Coordinates: Extract the coordinates of these points.
  3. Substitute Coordinates: Substitute the coordinates into the equation of Line AB.
  4. Verify Solutions: Confirm that the substituted coordinates satisfy the equation of Line AB.

1. Identify Points on Line AB:

  • Locate four distinct points where the line intersects the axes or stands out on the graph.

2. Determine Coordinates:

  • Note down the coordinates (x, y) of each identified point.

3. Substitute Coordinates:

  • Use the coordinates obtained to substitute into the equation of Line AB.
  • The equation of a line is typically in the form y = mx + b, where m is the slope and b is the y-intercept.

4. Verify Solutions:

  • Confirm that the substituted coordinates satisfy the equation of Line AB.
  • The substituted values should make the equation true when solved.

Example:

  • Suppose the equation representing Line AB is y = 2x + 3.
  • Points on the graph are (0, 3), (1, 5), (2, 7), and (-1, 1).
  • Substituting these coordinates into the equation:
    • For (0, 3): 3 = 2(0) + 3 (True)
    • For (1, 5): 5 = 2(1) + 3 (True)
    • For (2, 7): 7 = 2(2) + 3 (True)
    • For (-1, 1): 1 = 2(-1) + 3 (True)
  • All points satisfy the equation, confirming they lie on Line AB.

Conclusion:

  • By following these steps, you can find solutions of the equation representing Line AB from the provided graph.
 
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Linear Equation in Two Variables: for class-(ix)
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