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**3-5 Lines in the coordinate plane M11. B. 2. 2. 3. 11**

Lines in the coordinate plane M11.B A Objectives: 1)To graph lines given their equations 2) To write equations of lines

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Vocabulary The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept. Example: Y = 2x + 3 Y = 2x – 1 Y = 2x – 4

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**Example: Graph Lines in Slope-Intercept Form**

y = -2x + 4 y = ½ x -3 y = ¾ x

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Vocabulary Standard Form of a Linear Equation – is Ax + By = C, where A, B, and C are real numbers, and A and B are not both zero. Example: Find A, B and C. -3x + 2y = 12

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**Example: Graphing Lines Using Intercepts**

Use the x and y intercept to graph 4x – 6y =24 “Hide and Divide”

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**Example: Graphing Lines Using Intercepts**

Graph -2x + 4y = -8 Graph 5x – 6y = 30

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**Example: Transforming from Standard Form to Slope-Intercept Form**

Graph -6x + 3y = 12

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**Graph using Slope-Intercept Form**

-5x + y = -3 -6x – 3y = 12

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Vocabulary Point – Slope form – used for a nonvertical line through point (x₁ , y₁) where m = slope. y – y₁ = m( x – x₁)

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**Example: Using Point – Slope Form**

Write an equation of the line through point (3, 6) and with a slope of -8.

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**Using Point-Slope Form**

Example: Write an equation of the line with slope -1 that contains point P(2, -4)

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**Slope Formula Given two points: (x1, y1) and (x2, y2) m = y2 – y1**

x2 – x1 Example: Find the slope of (3, -2) and (-5, 6)

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**Example: Equation of a Line Given Two Points**

Write an equation of the line through points G( 4, -9 ) and H( -1, 1).

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**Equation of a Line Given Two Points**

Write an equation of the line that contains the points P(5, 0) and Q(7, -3).

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**Slopes of Special Lines**

What is the slope of a horizontal line and a vertical line?

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**Example: Equation of Horizontal & Vertical Lines**

Write equations for the horizontal line and the vertical line that contains P(3, 2).

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**Equations of Horizontal and Vertical Lines**

Write equations of the horizontal and vertical lines that contain the point P(5, -1)

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Section 3-5: Lines in the Coordinate Plane Goal 2.02: Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs.

Section 3-5: Lines in the Coordinate Plane Goal 2.02: Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs.

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