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.
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
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.
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