Given two points \((h,k)\) and \((p,q)\) the slope of the line passing through them may be generalised as \[ \frac{q-k}{p-h} \]
Slope-intercept form \[ y = mx + b \] Passes through \(y\) intercept at \(b\) with slope of \(m\).
Standard form \[ Ax + By = C \] Provides both \(x\) and \(y\) intercepts by setting \(A\) or \(B\) repectively to 0.
Point-slope form \[ y = m(x-h) + k \] Passes through \((h, k)\) with slope \(m\)
Linear system with parallel lines has no solution.
Colinear system has infite solutions.