Exercise 2.6 Class 9 Maths Solutions | Graphs of Linear Equations (Ganita Manjari)

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Exercise 2.6 introduces students to graphs of linear equations. It helps in understanding how the values of ‘a’ (slope) and ‘b’ (intercept) affect the graph of a straight line. This exercise builds a strong visual understanding of algebra.

Exercise 2.6 Solutions

Question 1

Draw the graphs of the following sets of lines. In each case, reflect on the role of ‘a’ and ‘b’.

(i) y=4x,  y=2x,  y=x

Solution

Graph of y equals 4x, y equals 2x and y equals x on coordinate plane showing positive slopes and origin intersection for Class 9 Maths Exercise 2.6
Graphs of linear equations y = 4x, y = 2x, and y = x showing positive slopes and passing through the origin.

ii) y=−6x,  y=−3x,  y=−xy = -6x,\; y = -3x,\; y = -x

solution

Graph of y equals minus 6x, y equals minus 3x and y equals minus x showing decreasing lines and origin intersection in Class 9 Maths
Graphs of linear equations y = -6x, y = -3x, and y = -x showing negative slopes and passing through the origin.

(iii) y=5x,  y=−5x

Solution

Graph of y equals 5x and y equals minus 5x showing positive and negative slopes with symmetry in Class 9 Maths Exercise 2.6
Graphs of y = 5x and y = -5x showing opposite slopes and symmetry about the origin.

Conclusion

This exercise helps students understand:

  • The role of slope (a) in determining steepness and direction
  • The role of intercept (b) in shifting the graph
  • Parallel lines (same slope)
  • Opposite slopes (reflection effect)

It builds strong graphing skills for future algebra and coordinate geometry.

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