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A Rule Makes Points

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 6 of 64.

An equation with x and y is a rule that turns each x into a y, and every pair it produces is a point. Take y = x + 2: at x = 0 it gives y = 2, at x = 1 it gives y = 3, at x = 2 it gives y = 4. Three inputs, three points: (0, 2), (1, 3), (2, 4).

$Three points made by y = x + 2$

Three points made by y = x + 2

Any x may be fed in, negatives included: at x = -3 the rule gives y = -1, so (-3, -1) belongs too. A rule holds infinitely many points; a table just shows a few of them.

Challenge

The rule is y = 2x - 1. Work out y at x = 0 and at x = 2, and place both points.

Try it yourself

y = 2x - 1

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 Up On 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