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The Corner of a Region

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 45 of 61.

The two boundary lines meet at a corner of their overlap region. Find that corner by solving the boundary equations together. For $y = x-1$ and $y = -x+3$ , set $x-1 = -x+3$ to get $x = 2$ , then $y = 1$ .

For these two inequalities, the intersection of the boundaries is included only if both boundaries are solid. With more inequalities, test each candidate intersection against every inequality. Some intersections may lie outside the solution region and therefore do not form its corners.

Challenge

Medium

A shaded region is drawn. Place the corner where its two boundary lines cross.

Try it yourself

Place the points

All lessons in Graphs & Systems

1Points and Rules

Two Numbers, One Point A Rule Makes Points The Points Line Up

4Slope-Intercept Form

y = mx + b The Starting Height Write the Equation Solve for y Draw From Any Form Recap: y = mx + b

7Parallel & Perpendicular

Same Slope, Never Meet The Perpendicular Slope A Right-Angle Line Recap: Two Relations

10Systems by Graphing

Two Lines, One Answer Solve by Drawing Check the Crossing When Lines Never Cross Recap: By Graphing

2The Whole Plane

The Four Quadrants Mirror Points On the Line or Not?Recap: Rule to Line

5Point-Slope Form

A Point and a Slope From Two Points Flat or Vertical Through Draw From a Point Recap: Point-Slope

8Function Notation

The Name of a Rule Inputs With Signs Find the Input The Graph of f Recap: f(x)

11Solving Systems Exactly

Substitution Isolate First Elimination Scale, Then Add Three Unknowns Two Numbers, Two Facts Recap: Two Methods

3Slope

Steepness as a Number Slope From Two Points Downhill Lines Flat and Straight Up A Fraction of a Slope Recap: Slope

6Standard Form

Ax + By = C The Two Intercepts Draw by Intercepts Between the Forms Recap: Standard Form

9Shaded Regions

A Line Splits the Plane Solid or Dashed Test a Point Rearrange, Then Shade Recap: Half-Planes Two Shadings OverlapThe Corner of a Region

12Final Challenges

Final: Round Trip Final: Where They Meet Final: Draw the Fence Final: The Whole Plane

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