CBSE · Class 6-12

Class 9 · Ganita Manjari

Unit 13 · Class 9Ganita Manjari

Two Variables, One Line

Linear equations in two variables — infinite solutions, one straight-line graph.

Lessons

3 concepts

1
Why Infinitely Many Solutions
Pick any $x$ , plug in, get a $y$ . Each choice gives another solution — the equation constrains only ONE quantity, so ONE degree of freedom remains.
2
Slope — the Heartbeat of a Line
Slope $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ tells you how fast $y$ changes with $x$ . Positive $m$ climbs left-to-right; negative $m$ falls; $m = 0$ is flat.
3
Two Lines, Three Fates
For lines $y = m_1 x + c_1$ and $y = m_2 x + c_2$ : same slopes, different intercepts $\to$ parallel. Same slopes, same intercept $\to$ same line. Different slopes $\to$ exactly one intersection.

Skills to practise

Skill · medium

Two Variables, One Line — Practice