# A.5bc - Linear Inequalities

A.5  The student will

b)  represent the solution of linear inequalities in two variables graphically;

c)  solve practical problems involving inequalities;

### BIG IDEAS

• I can master the challenge of a ski slope for snowboarding, determine the gradient of a road, figure the pitch of a roof, and build a handicap accessible ramp to a door.
• I will understand slope is rate of change where one value changing proportionately effects the other value, and the pattern of this relationship can be represented by a line that facilitates analysis and prediction.

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - AI.5 Understanding

·  A solution to an inequality is the value or set of values that can be substituted to make the inequality true.

·  The graph of the solutions of a linear inequality is a half-plane bounded by the graph of its related linear equation.  Points on the boundary are included unless the inequality contains only < or > (no equality condition).

·  Practical problems may be modeled and solved using linear inequalities.

·  Solutions and intervals may be expressed in different formats, including set notation or using equations and inequalities.

-  Examples may include:

 Equation/ Inequality Set Notation x = 3 {3} x = 3 or x = 5 {3, 5} y≥ 3 {y: y ≥ 3} Empty (null) set ∅ { }

·  Properties of Real Numbers and Properties of Inequality are applied to solve inequalities.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  A.5bRepresent the solution of a linear inequality in two variables graphically.

·  A.5cSolve practical problems involving linear inequalities.

·  A.5cDetermine whether a coordinate pair is a solution of a linear inequality or a system of linear inequalities.

·  A.5bdDetermine and verify algebraic solutions using a graphing utility.

### KEY VOCABULARY

parent function, transformations, slope, intercepts, coordinates, graph, positive slope, negative slope, zero slope, undefined slope, equation of a line, vertical, horizontal, dilations, reflections, translation, rate of change, dependent variable, independent variable, boundary, parallel, perpendicular

Updated: Jul 30, 2019