Class 9 · Chapter 13
Two Variables, One Line
Linear equations in two variables — infinite solutions, one straight-line graph.
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Ganita Manjari · Class 9 (2026-27)
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Detailed theory
Pick any , plug in, get a . Each choice gives another solution — the equation constrains only ONE quantity, so ONE degree of freedom remains.
Key concepts & formulas
01
General form: where are not both zero.
02
A solution is an ordered pair satisfying the equation — there are infinitely many.
03
Plotted, every solution lies on a single **straight line**; that line IS the equation.
04
Slope-intercept form: ; = slope, = -intercept.
05
is a horizontal line; is vertical.
06
Two lines can meet at one point (unique solution), never (no solution — parallel), or coincide (infinitely many).