Linear Inequalities in Two Variables

Vocabulary flashcards covering core definitions, graphing rules, and key example problems for linear inequalities in two variables.

Linear Inequality

A linear relation between two variables using an inequality symbol.

Boundary Line

The set of points where the two sides of a two-variable linear inequality are equal.

Linear Inequality in Two Variables

A relation between two variables using an inequality symbol, such as $y > 2x - 4$, whose graph is the region of the coordinate plane bounded by a boundary line.

Solid Boundary Line

A boundary line drawn on a coordinate plane when the inequality symbol is $\le$ or $\ge$.

Dashed Boundary Line

A boundary line drawn on a coordinate plane when the inequality symbol is $<$ or $>$.

Slope-Intercept Shading Rule

For an inequality in slope-intercept form, shade the region above the boundary line if the symbol is $>$ or $\ge$, and shade the region below the line if the symbol is $<$ or $\le$.

Test Point Method

A method used when an inequality is not in slope-intercept form, where a point not on the boundary line is tested; if it satisfies the inequality, shade the region containing it, otherwise shade the region that does not contain it.

Inequality Reversal Rule

The rule stating that when multiplying or dividing both sides of an inequality by a negative number, the inequality symbol must be reversed.

Graphing $y > \frac{2}{3}x - 1$ and $y \le 3$

Examples of graphing inequalities where $y > \frac{2}{3}x - 1$ uses a dashed line shaded above, and $y \le 3$ uses a solid horizontal line shaded below.

Graphing $x + 4y \ge 8$ Using Intercepts

A method where the $x$-intercept is $8$ and $y$-intercept is $2$, a solid boundary line is drawn, and the region excluding $(0, 0)$ is shaded because $0 \ge 8$ is false.

Spanish Club Fundraising Inequality

The linear inequality $10x + 8y \ge 640$ representing tee shirts sold at $\$10$ ($x$) and hats sold at $\$8$ ($y$) to make at least $\$640$, requiring at least $18$ hats if $50$ tee shirts are sold.

Solving $\frac{5}{2}(x - y) > 5$ for $y$

The algebraic procedure of multiplying both sides by $\frac{2}{5}$, subtracting $x$, and multiplying by $-1$ to reverse the inequality symbol, yielding $y < x - 2$.