Math 1 · Unit 5 · Lesson 2
Which Side to Shade
One procedure you can run every time: solve for y (flipping the sign if you multiply or divide by a negative), graph the boundary from m and b, dash it or make it solid, shade above for y greater and below for y less, and confirm with a test point. Above and below are not a rule to memorize: they are what greater and less mean once y is alone.
The big idea
Graphing a linear inequality is Unit 1 and Unit 3 in a row, plus one new step. Solve for y, and if you multiply or divide by a negative, flip the sign, exactly as in Unit 1. Graph the boundary from m and b, exactly as in Unit 3. Dash it for a strict sign and make it solid for an or-equal sign. Then shade: with y alone, y greater than the line means the higher points, so shade above, and y less than means the lower points, so shade below. That is not a memorized rule; it is what greater and less mean at the same x. Finally, put an easy test point such as (0, 0) into the original inequality to confirm the side. A vertical boundary shades right for x greater and left for x less; a horizontal one shades above or below.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with the five steps, the why behind above and below, the test point, the flip, the special cases, and a worked example. Plus a worksheet with grids and an answer key, and a short lesson plan.