Math 1 · Unit 5
Graphing Linear Inequalities in Two Variables
Four lessons: from a line to a region, which side to shade, match it and write it, and inequalities in the real world. An equation gives a line; an inequality gives a whole region with the same boundary line. Each card below opens a lesson. Every lesson has practice with hints, a study guide, a worksheet with an answer key, and a lesson plan.
From a Line to a Region
An equation gives a line; an inequality gives a whole region, one side of that line, called a half-plane. The boundary line comes from m and b as in Unit 3. The sign decides the edge: dashed for strict, solid for or-equal. Check points, sort signs, and see the region.
Start Unit 5, Lesson 1Which Side to Shade
One repeatable procedure: solve for y (flip if you multiply or divide by a negative), graph the boundary from m and b, dashed or solid, shade above for y greater and below for y less, then confirm with a test point. Includes the flip case and the vertical and horizontal special cases.
Start Unit 5, Lesson 2Match It and Write It
Read a region and write its inequality: the boundary gives m and b, dashed or solid gives strict or inclusive, the shaded side gives greater or less. Then match an inequality to its graph by elimination with the same three clues, boundary first, the Unit 3 habit with two more clues.
Start Unit 5, Lesson 3Inequalities in the Real World
A real limit becomes an inequality, and its region is every combination allowed: the boundary is the most you can do, inside is under the limit. Whole-things constraints turn the region into dots. Two limits at once overlap, which is Unit 6.
Start Unit 5, Lesson 4Printables for Unit 5
Study guides, worksheets with answer keys, and lesson plans for every lesson in this unit.