Slope–Intercept Line: y = mx + c

$m$ is the slope (rise over run) and $c$ is the y-intercept (where the line cuts the y-axis). So $y = 2x + 3$ rises by 2 units for every 1 unit right, and passes through $(0, 3)$. This is the most-used line form in board and JEE coordinate geometry.

Slide $m$ and $c$. The line rotates as you change $m$ and slides vertically as you change $c$. Set $m = 0$ to get a horizontal line; set $c = 0$ to make the line pass through the origin. The lab also reports the x-intercept $-c/m$.

Slope equals the tangent of the angle the line makes with the positive x-axis: $m = \tan\theta$. So $m = 1$ corresponds to $\theta = 45^\circ$, and $m = \sqrt{3}$ corresponds to $\theta = 60^\circ$. This connects coordinate geometry to trig — a favourite JEE crossover.

Parallel lines have equal slopes: $m_1 = m_2$. Perpendicular lines have slopes whose product is $-1$: $m_1 m_2 = -1$. So a line perpendicular to $y = 2x + 1$ has slope $-1/2$. The lab makes it easy to plot two lines and verify visually.