metadata
source: ncert_exercises
topic: algebra
class_level: class_9
chapter: ch4
exercise: ex4.4
difficulty: beginner
Class 9 | Ch4: Linear Equations in Two Variables | Exercise 4.4
Q1. Give geometric representations of y=3 as equation: (i) in one variable (ii) in two variables Answer: (i) In one variable (on number line): y=3 is a single point at 3 on the number line. ✅ (ii) In two variables: 0x+y=3. Graph is a horizontal line parallel to x-axis, passing through (0,3). ✅
Q2. Give geometric representations of 2x+9=0 as equation: (i) in one variable (ii) in two variables Answer: (i) In one variable: 2x+9=0 → x=-9/2=-4.5. Single point at -4.5 on number line. ✅ (ii) In two variables: 2x+0y+9=0. Graph is a vertical line parallel to y-axis, passing through (-9/2, 0) = (-4.5, 0). ✅
Key rules for graphs:
- y=k (constant): horizontal line parallel to x-axis at height k.
- x=k (constant): vertical line parallel to y-axis at distance k.
- y=0: the x-axis itself.
- x=0: the y-axis itself. ✅