Standard Form ax+by+c=0 MCQs Quiz | Class 9
This Class IX Mathematics (Code 041) quiz covers Unit II: Algebra. It focuses on Linear Equations in Two Variables, specifically the standard form ax+by+c=0. Test your ability to identify coefficients a, b, and c, and convert equations from other forms. Submit your answers to check your score and download the PDF solution sheet.
Understanding Linear Equations in Two Variables
A linear equation in two variables is an equation that can be written in the form ax + by + c = 0, where a, b, and c are real numbers, and a and b are not both zero. This form is known as the standard form. Understanding this structure is crucial for Class 9 Algebra.
Key Concepts
- Standard Form: The equation must be arranged so that all terms are on the left-hand side (LHS) and zero is on the right-hand side (RHS).
- Coefficients: ‘a’ is the coefficient of x, ‘b’ is the coefficient of y, and ‘c’ is the constant term.
- Missing Variables: If a variable is missing, its coefficient is 0. For example, in 3x + 5 = 0, we can write it as 3x + 0y + 5 = 0.
- Conversion: To find a, b, and c, first rearrange the given equation into standard form.
Examples of Conversion
| Given Equation | Standard Form (ax+by+c=0) | Values of a, b, c |
|---|---|---|
| 2x = 5 | 2x + 0y – 5 = 0 | a=2, b=0, c=-5 |
| y – 2 = 0 | 0x + 1y – 2 = 0 | a=0, b=1, c=-2 |
| 4 = 5x – 3y | 5x – 3y – 4 = 0 | a=5, b=-3, c=-4 |
| x = -5 | 1x + 0y + 5 = 0 | a=1, b=0, c=5 |
Quick Revision Notes
- Always move terms from RHS to LHS changing their signs.
- Ensure the order is x term, then y term, then constant.
- If ‘y’ is missing, write ‘0y’. If ‘x’ is missing, write ‘0x’.
- The graph of a linear equation in two variables is always a straight line.
Extra Practice Questions
- Write x = 3y in standard form.
- Identify a, b, c in the equation 2x + 3y = 9.35.
- Express y = x/2 as a linear equation in standard form.
- Find the value of k if x=1, y=1 is a solution of 2x + 3y = k.
- Write the equation of a line parallel to the x-axis at a distance of 3 units above it.
Content created and reviewed by the CBSE Quiz Editorial Team based on the latest NCERT textbooks and CBSE syllabus. Our goal is to help students practice concepts clearly, confidently, and exam-ready through well-structured MCQs and revision content.