Representing Inequalities as Regions Flashcards

All 5 cards in this deck

When drawing the boundary line for an inequality on a grid, when do you use a dashed (broken) line and when a solid line?

Dashed for strict inequalities ($<$ or $>$); solid for $\le$ or $\ge$.

What boundary line do you draw for the inequality $3x + 2y \ge 6$?

The solid line $3x + 2y = 6$ (replace the inequality sign with $=$).

How do you decide which side of a boundary line to shade?

e.g. $y \le 2x$

Substitute a test point not on the line, e.g. $(1, 0)$: $0 \le 2$ is true, so shade the side containing $(1,0)$.

What are the steps to shade the region satisfying a set of inequalities?

e.g. $y \ge 1$, $x + y \le 5$, $y \le 2x$

1. Draw each boundary line: $y = 1$, $x + y = 5$, $y = 2x$ (all solid here).
2. Test a point for each inequality to find the wanted side.
3. Shade the region satisfying all three and label it $R$.

True or false? A point lying exactly on a dashed boundary line is part of the region.

False. A dashed line means the boundary is not included; only a solid line ($\le$ or $\ge$) includes its points.