Graph of Linear Equation in Two Variables MCQs Quiz | Class 9
This quiz addresses Class IX Mathematics (Code 041) Unit II: Algebra, with a specific focus on the Graph of Linear Equation in Two Variables. The questions cover concepts such as plotting points on a Cartesian plane, verifying solutions, and understanding that the graph of a linear equation in two variables always forms a straight line. Complete the quiz to test your skills, check your score, and download a PDF answer sheet for future revision.
Understanding the Graph of Linear Equations
A linear equation in two variables is an algebraic equation of the form ax + by + c = 0, where a, b, and c are real numbers, and a and b are not both zero. The fundamental characteristic of such an equation is that its graph on a Cartesian plane is always a straight line.
Key Concepts
- Infinite Solutions: Every linear equation in two variables has infinitely many solutions. Each solution corresponds to a unique point on the line representing the equation.
- The Straight Line: All points that satisfy the equation lie on the same straight line. Conversely, every point on the line is a solution to the equation.
- Plotting Points: To graph an equation, find at least two solutions (coordinates), plot them on the graph paper, and draw a line passing through them. It is often recommended to plot three points to ensure accuracy.
Special Cases
| Equation Type | Graph Characteristic |
|---|---|
| x = a | A straight line parallel to the Y-axis. |
| y = b | A straight line parallel to the X-axis. |
| y = mx | A straight line passing through the origin (0,0). |
| y = 0 | The equation of the X-axis itself. |
| x = 0 | The equation of the Y-axis itself. |
Quick Revision Notes
- The graph of x = 0 is the y-axis.
- The graph of y = 0 is the x-axis.
- An equation of the type y = kx always passes through the origin.
- A linear equation in two variables cuts the coordinate axes at distinct points unless it passes through the origin.
Extra Practice Questions
- Draw the graph of x + y = 7.
- Give the equations of two lines passing through (2, 14). How many more such lines are there?
- If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.
- Determine whether the point (2, 3) lies on the line x + y = 5.
- Draw the graph of the equation 2x + y = 6 and find the coordinates where the line cuts the x-axis and y-axis.
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