Rearrange, Then Shade
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 45 of 64.
Unarranged inequalities are rearranged exactly like unarranged equations, with the one flip rule from the Inequalities section along for the ride. 2x + y <= 3 becomes y <= -2x + 3 (no flip, the y term was positive), and now it reads: boundary y = -2x + 3, solid, shaded below.
A flip appears only when both sides are divided by a negative, say from -y < x - 2 to y > -x + 2. The plane inherits every algebra rule the number line taught.
Challenge
Rearrange y - 1 > 2x in your head, then shade its solutions.
Try it yourself
Draw the graph
Test yourselfThis 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 PointThe Four QuadrantsPoints on the AxesMirror PointsRecap: The Plane4Slope-Intercept Form
y = mx + bThe Starting HeightWrite the EquationSolve for yDraw From Any FormRecap: y = mx + b7Parallel & Perpendicular
Same Slope, Never MeetThe Perpendicular SlopeA Right-Angle LineRecap: Two Relations2From Rule to Line
A Rule Makes PointsThe Points Line UpOn the Line or Not?Between the DotsRecap: Rule to Line