Finding Inequalities from Regions Flashcards

All 5 cards in this deck

What form do the equations of the vertical and horizontal boundary lines of a region take?

Vertical: $x = a$; horizontal: $y = b$.
e.g. $x = -3$ and $y = 6$.

Once you have the equation of a boundary line, how do you decide which inequality sign to use?

Substitute the coordinates of a point inside the shaded region and choose the sign that makes the statement true.

True or false? A dashed boundary line on a region means the inequality for that line uses $<$ or $>$.

True. Dashed excludes the boundary, so the inequality is strict.

How many inequalities do you need to write down to define a shaded region on a grid?

e.g. a region bounded by the four lines $y = 6$, $x = -3$, $y = 3x + 6$ and $y = -\frac{x}{2} + 1$

One inequality for each boundary line, so four here.

True or false? A shaded region lying above the solid boundary line $y = x$ is described by the inequality $y \ge x$.

True. Points above the line have $y$ greater than $x$, and a solid line includes the boundary, so $\ge$.