Lines · Andromeda

Definition

A line is a straight, one-dimensional figure that extends infinitely in both directions.

Lines represent the simplest mathematical relationship between variables (linearity), which is the first step in modeling data.

Equations of a Line:
- Slope-Intercept: $y = mx + b$
- Point-Slope: $y - y_1 = m(x - x_1)$
- General Form: $Ax + By = C$
- How to read: “y equals m x plus b; y minus y one equals m times the quantity x minus x one; and A x plus B y equals C.”
- Meaning: Different algebraic representations of a straight line on a Cartesian plane.
Parallel and Perpendicular Lines:
- Parallel lines have the same slope: $m_1 = m_2$ .
- Perpendicular lines have negative reciprocal slopes: $m_1 \cdot m_2 = -1$ .