Equations of Lines

A straight line drawn on a coordinate plane is fundamentally a physical record of constant change. Whether representing the steady depletion of a rocket’s fuel tank or a constant trajectory of light through a vacuum, every straight line is governed by a strict, unchanging relationship between its vertical and horizontal movement. The algebraic equations we use to capture these lines are not arbitrary strings of symbols; they are precise sets of instructions. If you know a line's starting position and its trajectory, or merely two distinct positions it passes through, you possess the necessary constraints to rebuild that line in its entirety. Our task is to translate the geometry of a drawn line into the elegant algebraic language of slope-intercept and point-slope forms.