Class 9 Maths Chapter 4 Linear Equations in Two Variables – Exercise 4.1 NCERT Solutions

Introduction

Exercise 4.1 introduces linear equations in two variables. You’ll learn how to represent real‑life situations mathematically, form equations, and understand the concept of variables and constants.

Key Concept

• General Form of Linear Equation in Two Variables:

$$$$ax+by+c=0

where $a,b,c$ are real numbers, and $a,b\mathrm{\ne }0$.

Solved Questions (Step by Step)

Q1. Write the equation of a line parallel to x‑axis and passing through $(0,2)$.

Solution:

• Equation of line parallel to x‑axis: $y=k$.

• Here, $k=2$.

• Final equation: $y=2$.

Q2. Write the equation of a line parallel to y‑axis and passing through $(3,0)$.

Solution:

• Equation of line parallel to y‑axis: $x=k$.

• Here, $k=3$.

• Final equation: $x=3$.

Q3. Write the equation of a line passing through $(0,0)$ with slope 1.

Solution:

• Equation: $y=mx$.

• Here, $m=1$.

• Final equation: $y=x$.

Q4. Write the equation of a line passing through $(0,0)$ with slope 2.

Solution:

• Equation: $y=mx$.

• Here, $m=2$.

• Final equation: $y=2x$.

Q5. Write the equation of a line passing through $(0,0)$ with slope $-1$.

Solution:

• Equation: $y=mx$.

• Here, $m=-1$.

• Final equation: $y=-x$.

Q6. Write the equation of a line passing through $(0,0)$ with slope $\frac{1}{2}$.

Solution:

• Equation: $y=mx$.

• Here, $m=\frac{1}{2}$.

• Final equation: $y=\frac{1}{2}x$.

Q7. Write the equation of a line passing through $(0,0)$ with slope $-2$.

Solution:

• Equation: $y=mx$.

• Here, $m=-2$.

• Final equation: $y=-2x$.

Q8. Write the equation of a line passing through $(0,0)$ with slope 3.

Solution:

• Equation: $y=mx$.

• Here, $m=3$.

• Final equation: $y=3x$.

Q9. Write the equation of a line passing through $(0,0)$ with slope $-\frac{1}{3}$.

Solution:

• Equation: $y=mx$.

• Here, $m=-\frac{1}{3}$.

• Final equation: $y=-\frac{1}{3}x$.

Q10. Write the equation of a line passing through $(0,0)$ with slope 4.

Solution:

• Equation: $y=mx$.

• Here, $m=4$.

• Final equation: $y=4x$.

Q11. Write the equation of a line passing through $(0,0)$ with slope $-4$.

Solution:

• Equation: $y=mx$.

• Here, $m=-4$.

• Final equation: $y=-4x$.

Q12. Write the equation of a line passing through $(0,0)$ with slope $\frac{3}{2}$.

Solution:

• Equation: $y=mx$.

• Here, $m=\frac{3}{2}$.

• Final equation: $y=\frac{3}{2}x$.

Q13. Write the equation of a line passing through $(0,0)$ with slope $-\frac{2}{3}$.

Solution:

• Equation: $y=mx$.

• Here, $m=-\frac{2}{3}$.

• Final equation: $y=-\frac{2}{3}x$.

Q14. Write the equation of a line passing through $(0,0)$ with slope 5.

Solution:

• Equation: $y=mx$.

• Here, $m=5$.

• Final equation: $y=5x$.

Q15. Write the equation of a line passing through $(0,0)$ with slope $-5$.

Solution:

• Equation: $y=mx$.

• Here, $m=-5$.

• Final equation: $y=-5x$.

FAQs (10 for Exercise 4.1)

1. Q: What is a linear equation in two variables? A: An equation of the form $ax+by+c=0$.

2. Q: How many solutions does a linear equation in two variables have? A: Infinitely many solutions, represented as points on a line.

3. Q: What is the slope of a line? A: The ratio of change in $y$ to change in $x$.

4. Q: What is the equation of a line parallel to x‑axis? A: $y=k$.

5. Q: What is the equation of a line parallel to y‑axis? A: $x=k$.

6. Q: What is the slope of line $y=mx$? A: Slope = $m$.

7. Q: What is the slope of line $y=0$? A: Slope = 0.

8. Q: What is the slope of line $x=0$? A: Undefined.

9. Q: How do you check if two lines are parallel? A: Compare slopes; if equal, lines are parallel.

10. Q: How do you check if two lines are perpendicular? A: Product of slopes = $-1$.

Conclusion

Exercise 4.1 has 15 questions that help you understand the basics of linear equations in two variables, slope, and equations of lines. This sets the foundation for solving simultaneous equations in later exercises.

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