Math 1 · Unit 5 · Lesson 2 · part 2 of 6
The repeatable procedure
Lesson 1 showed the region.
The repeatable procedure
Lesson 1 showed the region. This lesson gives you one procedure to draw it, every time, and the reason behind the one step people guess at: which side to shade.
- 1Solve for y, if you canGet y alone on the left, Unit 1 style. The one rule: if you multiply or divide both sides by a negative number, flip the inequality sign. The gator still eats the bigger number.
- 2Graph the boundary from m and bThe line with an equals sign. Plot b, step by m, as in Unit 3.
- 3Dashed or solidStrict (< or >): dashed. Or-equal (≤ or ≥): solid.
- 4Shade the sideWith y alone: y greater than the line means the points higher than the line, so shade above. y less than means lower, so shade below.
- 5Check with a test pointPick an easy point not on the line, usually (0, 0). Put it into the original inequality. True: shade its side. False: shade the other side. This confirms step 4; it does not replace it.
Why above and below are not a rule to memorizeTake any x. The line has one y there. A point at the same x is a solution of y > (the line) exactly when its y is bigger, and a bigger y is a higher point. So y greater than the line is literally the points above it, and y less than is the points below. Above and below are what greater and less mean once y is by itself.