Linear Equation in Two Variables

Any equation of the form $ax + by + c = 0$, where a, b are not both zero, is a linear equation in two variables. Its solution is any pair $(x, y)$ making the equation true. Geometrically these solutions form a straight line.

Slide a, b, c and the line redraws instantly. Set a = 2, b = 3, c = -6 to see the line passing through $(3, 0)$ and $(0, 2)$. Slide c alone to see the line translate without changing its slope.

Students sometimes plot only one solution and call it the answer. A linear equation in two variables has infinitely many solutions, all lying on the line. Always show at least two points and draw the full line in board answers.

If $50x + 80y = 400$ means x kg of rice at Rs 50 plus y kg of dal at Rs 80 totalling Rs 400, every valid grocery combination is a point on this line. The lab makes such trade-offs visual.