Mathematics solution NCERT
Class 9 - Chapter 2: Introduction to Linear Polynomials
Graphs of Linear Equations
(i) y = 4x, y = 2x, y = x
Observation:
- All lines pass through the origin because b = 0.
- As the value of a increases, the line becomes steeper.
- y = 4x is steepest and y = x is least steep.
(ii) y = -6x, y = -3x, y = -x
Observation:
- All lines pass through the origin.
- Negative slope causes the graph to fall from left to right.
- Larger negative values produce steeper downward lines.
(iii) y = 5x, y = -5x
Observation:
- Both lines have the same steepness.
- One rises and the other falls.
- Both pass through the origin.
(iv) y = 3x - 1, y = 3x, y = 3x + 1
Observation:
- All lines have the same slope (a = 3).
- The lines are parallel.
- Changing b shifts the graph vertically.
(v) y = -2x - 3, y = -2x, y = 2x + 3
Observation:
- First two lines are parallel because they have the same slope.
- Changing b shifts the graph up or down.
- Positive slope rises while negative slope falls.