Math - 2018-19
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
· 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.5b_{1 }Represent the solution of a linear inequality in two variables graphically.
· A.5c_{1 }Solve practical problems involving linear inequalities.
· A.5c_{2 }Determine whether a coordinate pair is a solution of a linear inequality or a system of linear inequalities.
· A.5bd_{1 }Determine 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