Graphing Inequalities Flashcards

All 10 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.

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 $\ge$.