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The Points Line Up

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 7 of 64.

Plot enough points of y = x + 2 and something remarkable shows: they all fall on one straight line. That is no accident. Every equation of the shape y = (number)x + (number) draws a line, which is why it is called a linear equation.

$Every point of y = x + 2 falls on one line$

Every point of y = x + 2 falls on one line

The line IS the equation, drawn: every point on the line satisfies the rule, and every pair satisfying the rule lies on the line. Two points are enough to pin a line down, so drawing one takes exactly two well-chosen points.

Challenge

Draw the line y = x - 2.

Try it yourself

y = x - 2

Draw the graph

Test yourself

This 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 Point The Four Quadrants Points on the Axes Mirror Points Recap: The Plane

4Slope-Intercept Form

y = mx + b The Starting Height Write the Equation Solve for y Draw From Any Form Recap: y = mx + b

7Parallel & Perpendicular

Same Slope, Never Meet The Perpendicular Slope A Right-Angle Line Recap: Two Relations

10Systems by Graphing

Two Lines, One Answer Solve by Drawing Check the Crossing When Lines Never Cross Recap: By Graphing

2From Rule to Line

A Rule Makes PointsThe Points Line UpOn the Line or Not?Between the Dots Recap: Rule to Line

5Point-Slope Form

A Point and a Slope From Two Points Flat or Vertical Through Draw From a Point Recap: Point-Slope

8Function Notation

The Name of a Rule Inputs With Signs Find the Input The Graph of f Recap: f(x)

11Solving Systems Exactly

Substitution Isolate First Elimination Scale, Then Add Three Unknowns Two Numbers, Two Facts Recap: Two Methods