From Two Points
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 24 of 64.
Two points hand over a line in two moves: slope first, then point-slope with either point. Through (1, 2) and (3, 8):
m = (8 - 2)/(3 - 1) = 3
y - 2 = 3(x - 1)
y = 3x - 1
Using the other point instead, y - 8 = 3(x - 3), expands to the very same y = 3x - 1: the line does not care which of its points introduced it.
This is the complete recipe for "find the equation of the line through these two points", the most asked question of the chapter.
Challenge
Find the equation of the line through (1, 3) and (4, 9).
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Graphs & Systems
1The Coordinate Plane
Two Numbers, One PointThe Four QuadrantsPoints on the AxesMirror PointsRecap: The Plane4Slope-Intercept Form
y = mx + bThe Starting HeightWrite the EquationSolve for yDraw From Any FormRecap: y = mx + b7Parallel & Perpendicular
Same Slope, Never MeetThe Perpendicular SlopeA Right-Angle LineRecap: Two Relations2From Rule to Line
A Rule Makes PointsThe Points Line UpOn the Line or Not?Between the DotsRecap: Rule to Line5Point-Slope Form
A Point and a SlopeFrom Two PointsFlat or Vertical ThroughDraw From a PointRecap: Point-Slope