default_background
✕

Find the best tutors and institutes for Class 10 Tuition

Find Best Class 10 Tuition

Please select a Category.

Please select a Locality.

No matching category found.

No matching Locality found.

Q2(vi):
Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case: (vi) $3x + 2 = 0$

Solution :

Initial Setup & Given Equation

We are given the linear equation:

$3x + 2 = 0$

The objective is to express this equation in the standard two-variable form, $ax + by + c = 0$, and to identify the corresponding real coefficients $a$, $b$, and $c$.

Step 1: Algebraic Transformation to Standard Form

The standard form of a linear equation in two variables is defined as:

$ax + by + c = 0$

where $x$ and $y$ are variables, and $a$, $b$, and $c$ are real numbers such that $a$ and $b$ are not simultaneously zero [Per the fundamental definition of a linear equation in two variables].

Observing the given equation $3x + 2 = 0$, we note the absence of the $y$-variable. To represent this equation in a two-variable format without altering its mathematical equivalence, we introduce the variable $y$ with a coefficient of $0$. [Since $0 \cdot y = 0$ for any real number $y$, the additive identity property ensures the equation's value remains unchanged].

Rewriting the equation yields:

$3x + 0 \cdot y + 2 = 0$

Step 2: Extraction of Coefficients

By aligning our transformed equation directly with the standard form, we can map the corresponding coefficients:

  • Standard Form: $ax + by + c = 0$
  • Transformed Equation: $3x + 0y + 2 = 0$

Comparing the terms positionally:

  • The coefficient of $x$ is $a = 3$.
  • The coefficient of $y$ is $b = 0$.
  • The constant term is $c = 2$.

Geometric Interpretation (Graphical Representation)

Geometrically, solving the equation $3x + 2 = 0$ for $x$ yields $x = -\frac{2}{3}$. In a two-dimensional Cartesian coordinate system, an equation of the form $x = k$ (where $k$ is a constant) represents a vertical line parallel to the $y$-axis. The line intersects the $x$-axis at the coordinate $(-\frac{2}{3}, 0)$. Because $y$ can take any real value while $x$ remains constant, the coefficient of $y$ is effectively zero.

x y O -1 -2 1 3x + 2 = 0 (-2/3, 0)

Final Conclusion

Final Solution: The equation expressed in the standard form $ax + by + c = 0$ is $3x + 0y + 2 = 0$. The corresponding coefficients are $a = 3$, $b = 0$, and $c = 2$.


More Questions from Class 9 Mathematics Linear Equations in Two Variables EXERCISE 4.1


CBSE Solutions for Class 9 Mathematics Linear Equations in Two Variables


Chapters in CBSE - Class 9 Mathematics


Top Tutors who teach Linear Equations in Two Variables

Fundamend Academy Class 10 Tuition institute in Doddaballapura
(16)
Top Tutor
locationImg SH 74, Doddaballapura
experience Less than a yr Exp students 3 students
greenClock 703 hrs of classes completed
rsIcon 650 per hour
We take the burden off your shoulders so your child succeeds. No fake promises, just real progress.
Online Classes Online Classes

Your Hard Work. Their Future. Our Responsibility. At Fundamend Academy, we know that every penny you spend on tuition is a penny earned through sacrifice. You aren't just looking for "classes"—you are looking for a teacher who cares as much as you do. Why Fundamend Academy? We’ve removed the risks that usually waste your money and time: Money-Back Peace of Mind: If your child doesn't "click" with their teacher, we swap the tutor immediately at zero extra cost. Your fees will never go to waste. (1) Zero Hidden Costs: All study materials, board exam test series, and session recordings are included. No extra books to buy. (2) Total Honesty: No fake promises. You get a weekly report and a monthly call to discuss your child’s real progress. (3) The Comfort of Home Language: We teach in your child’s native tongue so they finally understand the concept instead of just memorizing it. We don’t just teach; we take the burden off your shoulders so you can see your child succeed. BOOK A FREE DEMO See our teaching for yourself before you spend a single rupee.

Ramya Rajesh

I thank from my bottom of my heart to Girish Sir for identifying the gaps in my son, now he secured excellent marks in his boards. Thanks for all the tutors. I can't forget this. I strongly recommend my friends, relatives .

Skills: English , Mathematics and more
Also teaches: Kannada Language, Class 9 Tuition and more

Rahul Verma Class 10 Tuition trainer in Delhi
(339)
superTutorSuper Tutor
locationImg Shahdara Chitrakoot, Delhi
experience 10 yrs of Exp students 74 students
greenClock 7161 hrs of classes completed
rsIcon 500 per hour
Empowering Minds in Mathematics, Science, and Web Development
Online Classes Online Classes

With extensive experience in providing Class 10 tuition, I specialize in teaching mathematics, science, and computer science. My approach emphasizes a thorough understanding of key concepts and practical applications. In mathematics, I cover topics such as algebra, geometry, and trigonometry. My science classes include physics, chemistry, and biology, focusing on fundamental principles and real-world relevance. In computer science, I teach programming basics, algorithms, and data management. I use interactive tools, clear presentations, and regular assessments to ensure comprehensive learning. My goal is to build strong foundational knowledge, boost confidence, and prepare students for their board exams and future academic pursuits.

Sanjali Mishra

I’m really glad I found Rahul sir through UrbanPro. He has been extremely helpful with my Computer studies and has made understanding different concepts so much easier for me. He is very patient while explaining things and always makes sure that I actually understand the topic instead of just memorising it. I started taking his help after my Unit Tests, and it has genuinely made a big difference. With my half-yearlies coming up, I feel much more prepared and confident in Computer, and a lot of that is because of his guidance and support. He has helped me improve so much and has always been really supportive whenever I’ve had doubts. I’m really thankful for all his help and would definitely recommend him to anyone looking for a Computer tutor!

Skills: Information and Comunication Technology , Computer Practices and more
Also teaches: Node.JS, MongoDB and more

(20)
Top Tutor
locationImg Uttorayon Township, Siliguri
experience 3 yrs of Exp students 3 students
greenClock 91 hrs of classes completed
rsIcon 350 per hour
Knowledge and experience is everything 1stly take a demo and you will get to know what i Teach
Online Classes Online Classes
homeTutions Student's Home
regularClasses Tutor's home

Ability to connect with children (or with older students), on a personal level. communication and social skills.Teaching can be quite satisfying for people who do it well. I know this because I am a teacher, too. Although I do not think I'm always the best teacher, do I know that the majority of my students love me, and I guess this is partly why good things happen in my classroom. I have spent a lot of time thinking about and done a lot of research in to the question of what characteristics make a teacher effective and how I can succeed in the classroom. Although every great teacher has their own special, unique style, I have found that there are nine specific universal qualities that are necessary for anyone who wants to teach effectively, whether they want to teach in an elementary school or a university. If any teacher possesses the following characteristics and qualities, he/she can become a very good teacher with large fan base.

Skills: Mathematics , Physics and more
Also teaches: Class 7 Tuition, Class 9 Tuition and more

locationImg Carterpuri, Palam Vihar, Gurgaon
experience 20 yrs of Exp
rsIcon 500 per hour
Learning forever
homeTutions Student's Home

I am a professional teacher with more than 25 years of teaching experience in prestigious schools of India.My teaching assures value for money and produce best results.I emphasize on concepts clarity and create natural interest in the subject.

Skills: Mathematics , Physics and more
Also teaches: Class 6 Tuition, Class 12 Tuition and more

(2)
Top Tutor
locationImg Sector 49 South City II, Gurgaon
experience 16 yrs of Exp
rsIcon 500 per hour
I am an engineer. I teach maths and science. I am teaching for the last 16 years
Online Classes Online Classes
homeTutions Student's Home

I am an engineer and i have been teaching for the past 16 years. I put stress on the clarification of the basic concepts of the subject. I teach maths and science.

Skills: Mathematics , Science
Also teaches: Class 6 Tuition, Class 9 Tuition and more

Find more Tutor for Linear Equations in Two Variables in your City


Other Subjects in CBSE - Class 9

Worksheet Icon

Download free CBSE - Class 9 Mathematics Linear Equations in Two Variables EXERCISE 4.1 worksheets

Download Now

Find Best Class 10 Tuition ?

Find Now »