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The Coordinate Plane and Graphing

Plot points in all four quadrants and graph linear equations.

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The Coordinate Plane and Graphing

Four Quadrants

The coordinate plane is divided into four quadrants:

QuadrantxxyyExample
I++(3,2)(3, 2)
II–+(−3,2)(-3, 2)
III––(−3,−2)(-3, -2)
IV+–(3,−2)(3, -2)

Graphing Linear Equations

A linear equation graphs as a straight line.

To graph y=2x−1y = 2x - 1:

xxy=2x−1y = 2x - 1Point
-12(−1)−1=−32(-1) - 1 = -3(−1,−3)(-1, -3)
02(0)−1=−12(0) - 1 = -1(0,−1)(0, -1)
12(1)−1=12(1) - 1 = 1(1,1)(1, 1)
22(2)−1=32(2) - 1 = 3(2,3)(2, 3)

Plot the points and connect them with a straight line.

X-intercept and Y-intercept

  • Y-intercept: Where the line crosses the y-axis (x=0x = 0)
  • X-intercept: Where the line crosses the x-axis (y=0y = 0)

For y=2x−4y = 2x - 4:

  • Y-intercept: (0,−4)(0, -4)
  • X-intercept: Set y=0y = 0: 0=2x−4  ⟹  x=20 = 2x - 4 \implies x = 2, so (2,0)(2, 0)

Horizontal and Vertical Lines

  • Horizontal: y=cy = c (example: y=3y = 3)
  • Vertical: x=cx = c (example: x=−2x = -2)

Distance on the Coordinate Plane

For horizontal/vertical distances, subtract coordinates:

  • Distance from (1,3)(1, 3) to (5,3)(5, 3): ∣5−1∣=4|5 - 1| = 4 units

Practice: Graph y=−x+3y = -x + 3 by making a table of values. Find the x-intercept and y-intercept.

Explain using:

⚠️ Common Mistakes: The Coordinate Plane and Graphing

Avoid these 3 frequent errors

🌍 Real-World Applications: The Coordinate Plane and Graphing

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📝 Worked Example: Solving a Quadratic by Factoring

Problem:

Solve x2−5x+6=0x^2 - 5x + 6 = 0.

2Factor the quadratic
3Set each factor equal to zero
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❓ Frequently Asked Questions

What is The Coordinate Plane and Graphing?▾
Plot points in all four quadrants and graph linear equations.
How can I study The Coordinate Plane and Graphing effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Regular review and active practice are key to retention.
Is this The Coordinate Plane and Graphing study guide free?▾
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What course covers The Coordinate Plane and Graphing?▾
The Coordinate Plane and Graphing is part of the Pre-Algebra course on Study Mondo, specifically in the Introduction to Graphing section. You can explore the full course for more related topics and practice resources.