Rearrange, Then Shade
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 45 of 64.
When y is not alone on the left, solve for y first, the same way you rearrange an equation. The only extra rule is the flip rule for inequalities. To rearrange 2x + y <= 3, subtract 2x from both sides to get y <= -2x + 3. There is no flip, because you did not multiply or divide by a negative. Now you can read the graph from it. The boundary line is y = -2x + 3, it is solid, and the shading is below it.
The sign flips only when you multiply or divide both sides by a negative number. For example, dividing -y < x - 2 by -1 gives y > -x + 2. Every rule for rearranging an inequality on the number line also holds for an inequality in x and y.
Challenge
MediumRearrange y - 1 > 2x to get y alone, 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