3-5 Lines in the coordinate plane M11. B. 2. 2. 3. 11 3-5 Lines in the coordinate plane M11.B.2 2.3.11.A Objectives: 1)To graph lines given their equations 2) To write equations of lines

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

Example: Graph Lines in Slope-Intercept Form y = -2x + 4 y = ½ x -3 y = ¾ x

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

Example: Graphing Lines Using Intercepts Use the x and y intercept to graph 4x – 6y =24 “Hide and Divide”

Example: Graphing Lines Using Intercepts Graph -2x + 4y = -8 Graph 5x – 6y = 30

Example: Transforming from Standard Form to Slope-Intercept Form Graph -6x + 3y = 12

Graph using Slope-Intercept Form -5x + y = -3 -6x – 3y = 12

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

Example: Using Point – Slope Form Write an equation of the line through point (3, 6) and with a slope of -8.

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

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)

Example: Equation of a Line Given Two Points Write an equation of the line through points G( 4, -9 ) and H( -1, 1).

Equation of a Line Given Two Points Write an equation of the line that contains the points P(5, 0) and Q(7, -3).

Slopes of Special Lines What is the slope of a horizontal line and a vertical line?

Example: Equation of Horizontal & Vertical Lines Write equations for the horizontal line and the vertical line that contains P(3, 2).

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