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Between the Dots

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 9 of 64.

A line does not skip from lattice point to lattice point; it passes through everything in between. On y = 1/2x + 1 the input x = 1 gives y = 3/2, a perfectly good point half a step up from 1. Rules with fractions land between the grid dots, and the line runs through them all the same.

$y = 1/2x + 1 climbs half a step per step$

y = 1/2x + 1 climbs half a step per step

When drawing such a line, chase whole-number points: x = 0, 2, 4 give y = 1, 2, 3 with no fractions in sight. Even x values tame a 1/2 the way multiples of 3 tame a 1/3.

Challenge

Draw the line y = 1/2x - 1.

Try it yourself

y = 1/2x - 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 Points The Points Line Up On the Line or Not?Between the DotsRecap: 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