Week 3 Graphing Linear Inequalities - Vocabulary Flashcards

A set of vocabulary flashcards covering key concepts from Week 3: Graphing Linear Inequalities, including boundary concepts, shading, systems, and linear programming.

Linear inequality in two variables

An inequality of the form ax + by ≤, ≥,

Solution set to a linear inequality

All ordered pairs (x,y) that satisfy the inequality.

Boundary line

The line obtained by replacing the inequality with its equality; separates shaded region from unshaded.

Shaded region

The portion of the plane containing the solutions to the inequality; determined by the inequality sign and test point.

Feasible region

The set of all points that satisfy every inequality in a system; represents potential solutions.

Slope

The rate of change of y with respect to x on a line; rise over run.

y-intercept

The point where a line crosses the y-axis (x = 0); the value of y when x = 0.

Slope-intercept form

The equation of a line written as y = mx + b, where m is slope and b is the y-intercept.

Standard form

The linear equation written as Ax + By = C with A, B, C integers, often arranged with A ≥ 0.

Intercepts

The x-intercept (where y = 0) and y-intercept (where x = 0) of a boundary line.

Test point

A chosen point used to determine which side of the boundary is shaded (often the origin).

Solid boundary

A boundary line included in the solution (≤ or ≥); drawn as a solid line.

Dashed boundary

A boundary line not included in the solution ( < or > ); drawn as a dashed line.

System of two linear inequalities

Two inequalities whose solution is the intersection of their half-planes.

System of three linear inequalities

Three inequalities whose solution is the intersection of three half-planes.

Overlapping shaded region

The region common to all shaded half-planes, i.e., the solution to the system.

Intersection point

The point where boundary lines cross; a candidate vertex of the feasible region.

Vertex (corner point)

A point where two boundary lines intersect; often a potential optimal solution in linear programming.

Objective function

A linear function to be maximized or minimized, such as P = 3x + 4y or C = 2x + 5y.

Maximization

Finding the greatest possible value of the objective function under the constraints.

Minimization

Finding the smallest possible value of the objective function under the constraints.

Linear programming

A method to maximize or minimize a linear objective function subject to linear inequalities.

Word problem translation

Converting a real-world scenario into a system of linear inequalities.

Variables x and y

Common two-variable quantities representing quantities in an inequality or system; x and y denote the two coordinates or quantities.

Constraint

An inequality that restricts the values of variables in a problem.