Menu

Tech

English

Between the Forms

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 31 of 64.

The two forms are one line in two costumes, and the change of costume is the solve-for-y from chapter 4. Take 5x + 2y = 10: moving the 5x and dividing by 2 gives y = -5/2x + 5, and now the slope -5/2 is visible.

A shortcut worth knowing sits inside: for Ax + By = C the slope is always -A/B. It falls straight out of the rearrangement, and it turns "what is the slope of 3x - 2y = 8" into a one-line answer.

Challenge

Rewrite 2x + 6y = 12 in slope-intercept form: solve for y and multiply everything out.

Try it yourself

2x + 6y = 12

Solve for y

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 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