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Linear Equations in Two Variables Class 9 Maths — Revision Notes

This chapter covers linear equations with two variables and their graphical representations. Students learn to plot graphs and find solutions.

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TL;DR: This chapter covers linear equations with two variables and their graphical representations. Students learn to plot graphs and find solutions.

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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This chapter covers linear equations with two variables and their graphical representations. Students learn to plot graphs and find solutions.

Linear Equation Form

  • Standard form: ax + by + c = 0 where a, b, c are constants
  • Graph is straight line on coordinate plane
  • Slope-intercept form: y = mx + b where m is slope, b is y-intercept
  • Point-slope form: y - y1 = m(x - x1)

Graphing Linear Equations

  • Find two points satisfying equation
  • Plot points on coordinate plane
  • Draw straight line through points
  • x-intercept: point where line meets x-axis (y = 0)
  • y-intercept: point where line meets y-axis (x = 0)

Slope

  • Slope m = (y2 - y1) / (x2 - x1) = rise / run
  • Positive slope: line goes upward left to right
  • Negative slope: line goes downward left to right
  • Zero slope: horizontal line, Undefined slope: vertical line

Solutions

  • Solution: ordered pair (x, y) satisfying the equation
  • Equation has infinite solutions
  • Solution set is set of all ordered pairs satisfying equation
  • Graph represents solution set

Key Terms

  • Linear Equation: Equation of form ax + by + c = 0 with degree 1
  • Slope: Measure of steepness of line (rise/run)
  • Intercept: Point where line meets coordinate axis

Frequently Asked Questions

How do you find x-intercept and y-intercept?

For x-intercept, set y = 0 and solve for x. For y-intercept, set x = 0 and solve for y.

What is slope of line through (2,3) and (5,9)?

m = (9-3)/(5-2) = 6/3 = 2. Line has slope 2, meaning it rises 2 units for every 1 unit run.

More Class 9 Maths Revision Notes

  • Number Systems
  • Polynomials
  • Lines and Angles
  • Triangles

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