Problem preview

A-CED.3 Warmup M1-003-A04-V03

Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.

Graph a feasible region from inequalities

Problem

For \(x\le~4\), \(y\le~3\), \(x+y\ge~2\), \(x\ge~0\), \(y\ge~0\), identify boundary types, shading directions, and feasible-region vertices in counterclockwise order starting at \((2,0)\).

Coordinate graph showing the boundary lines for x less than or equal to 4, y less than or equal to 3, x plus y greater than or equal to 2, x nonnegative, and y nonnegative, without the feasible region shaded.

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boundaries = all solid; shading = x≤4, y≤3, x+y≤2, x≥0, y≥0; vertices = (0,0), (2,0), (0,2)

boundaries = all dashed; shading = x<4, y<3, x+y>2, x>0, y>0; vertices = (2,0), (4,0), (4,3), (0,3), (0,2)

boundaries = x=4 solid, y=3 solid, x+y=2 solid, x=0 solid, y=0 solid; shading = x≤4, y≤3, x+y≥2, x≥0, y≥0; vertices = (2,0), (4,0), (4,3), (0,3), (0,2)

boundaries = x=4, y=3, x+y=2 solid; shading = x≤4, y≤3, x+y≥2; vertices = (2,0), (4,0), (4,3), (0,3), (0,2)

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Curriculum context

Course: Math I
Standard: A-CED.3
Category: Algebra
Domain: Creating Equations
Objective: Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
Problem type: Graph a feasible region from inequalities