Mr. Integral

THE BIG IDEA

Analytic Geometry

How can a picture become an equation?

Coordinates let us describe a position precisely. Distances and slopes then turn those positions into measurements, and line equations capture a whole relationship at once.

Begin the first lesson →See the lesson route ↓

16 lessons · No deadlines or locked lessons

SEE THE CONNECTIONS

How the ideas fit together.

A map of the main ideas. Follow a node to its lesson.

  1. Start with01Position
  2. comparing positions gives02Distance & slope
  3. a constant slope defines03Line models
  4. combining models locates04Intersections

YOUR LEARNING ROUTE

One idea at a time.

Read the explanation, use the visualization, then try the check before opening its reasoning.

Keep the unit cheat sheet handy →
Coordinates and distance4 lessons
  1. 01The Coordinate PlaneTurn a point’s coordinates into a position on the plane.
  2. 02Regions of the PlaneUse signs and inequalities to describe a region.
  3. 03Distance Between Two PointsFind distance by identifying the horizontal and vertical changes.
  4. 04The Midpoint FormulaLocate a point halfway between two endpoints.
Slope and line equations5 lessons
  1. 05Defining SlopeInterpret slope as vertical change per unit horizontal change.
  2. 06Finding SlopeCalculate slope consistently from two points.
  3. 07Writing Line EquationsBuild a line equation from a point and a direction.
  4. 08Horizontal and Vertical LinesDistinguish horizontal and vertical line equations.
  5. 09Equations from InterceptsUse axis crossings to reconstruct a line.
Reading and comparing lines7 lessons
  1. 10Testing a Point Against a LineTest membership by substitution rather than visual guesswork.
  2. 11Intersection of Two LinesFind a point that satisfies two line equations at once.
  3. 12Graphing LinesGraph a line using an intercept and a slope.
  4. 13Relative Positions of Two LinesUse slopes and intercepts to compare two lines.
  5. 14Parallel LinesRecognize equal directions from line equations.
  6. 15Perpendicular LinesIdentify a right angle using the slope relationship.
  7. 16Coincident LinesRecognize different equations describing the same line.