A Rule Makes Points

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 2 of 61.

A plant is 1 cm tall and grows 1 cm a day. Write each day with its height as a pair of numbers. Each pair is a point on a grid.

Day 0: 1 cm, the point (0, 1)
Day 1: 2 cm, the point (1, 2)
Day 2: 3 cm, the point (2, 3)

The rule $y = x+1$ says: to get the height $y$ , add 1 to the day $x$ . Day 4 gives $y = 4+1 = 5$ , so the point is (4, 5). Every $x$ you pick gives one more point.

$The point (4, 5): day 4, 5 cm tall$

Challenge

The rule is $y = 2x-3$ . Work out $y$ for $x$ = 0, 1, 2 and 3, and place the four points. Drag each dot to its spot on the grid. What do you notice?

Try it yourself

y = 2x-3

Place the points

All lessons in Graphs & Systems

1Points and Rules

Two Numbers, One PointA Rule Makes PointsThe Points Line Up

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

2The Whole Plane

The Four Quadrants Mirror Points On the Line or Not?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