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3.5 Lines in the Coordinate Plane

3.5 Lines in the Coordinate Plane. Chapter 3: Parallel and Perpendicular Lines. 3.5 Lines in the Coordinate Plane. Slope-Intercept Form: y = mx + b m: slope b: y -intercept (x, y): point. Slope-Intercept Form. Identify the slope and y -intercept for each:

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3.5 Lines in the Coordinate Plane

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  1. 3.5 Lines in the Coordinate Plane Chapter 3: Parallel and Perpendicular Lines

  2. 3.5 Lines in the Coordinate Plane Slope-Intercept Form: y = mx + b m: slope b: y-intercept (x, y): point

  3. Slope-Intercept Form Identify the slope and y-intercept for each: a. y = 3x + 2 b. y = -2x + 5 c. y = ½x – 5 d. y = 3x – ½ e. y = -5x – 4 f. y = 0.2x + 0.7

  4. Graphing Lines in Slope-Intercept Form • Graph the line y = 3/4x + 2 m = b = • Graph the line y = x + 2 m = b = • Graph the line y = 3x + 4 m = b =

  5. Graphing Lines in Slope-Intercept Form • Graph the line y = -½x – 2 m = b = • Graph the line y = ½x – 1 m = b = • Graph the line y = -5/3 x + 2 m = b =

  6. Standard Form Ax + By = C (3x + 2y = 5) To Graph from Standard Form, find the x- and y- intercepts: To find the x-intercept, plug in 0 for y. To find the y-intercept, plug in 0 for x.

  7. Graphing Using Intercepts • Graph 6x + 3y = 12 Find the x-intercept: Find the y-intercept:

  8. Graphing Using Intercepts • Graph -2x + 4y = -8 Find the x-intercept: Find the y-intercept:

  9. Transforming to Slope-Intercept Form • Graph 4x – 2y = 9, using slope-intercept form:

  10. Transforming to Slope-Intercept Form • Graph -5x + y = -3, using slope-intercept form:

  11. Write each equation in slope-intercept form and graph the line: • y = 2x + 1 • y – 1 = x • y + 2x =4 • 8x + 4y = 16 • 2x + 6y = 6 • ¾x – ½y = 1/8

  12. Point-Slope Form y – y1 = m(x – x1) (1, 3) and slope 2: (y – 3) = 2(x – 1) y – y1 = m(x – x1)

  13. Using Point-Slope Form • Write an equation of the line through point P(-1, 4) with slope 3. y – y1 = m(x – x1) y – y1 = m(x – x1)

  14. Using Point-Slope Form • Write an equation of the line through point P(2, -4) with slope -1.

  15. Write an equation of the line in point-slope form: • P(2, 3), slope = 2 • I(4, -1), slope = 3 • R(-2, -6), slope = -4 • A(6, 1), slope = ½ • T(-3, 5), slope -1 • E(0, 4), slope 1

  16. Writing an Equation of a Line Given Two Points: • Write an equation of the line through A(-2,3) and B(1,-1): Find the slope: Use one point and write the equation in point-slope form:

  17. Writing an Equation of a Line Given Two Points: • Write an equation of the line through P(5,0) and Q(7,-3) Find the slope: Use one point and write the equation in point-slope form:

  18. Write an equation in point-slope form of the line that contains the given points: • D(0,5) E(5,8) • F(6,2) G(2,4) • H(2,6) I(-1,3) • J(-4,4) K(2,10) • L(-1,0) M(-3,-1) • N(8,10) O(-4,2)

  19. Equations of Horizontal and Vertical Lines: • A Horizontal Line cuts through the y-axis, so the equation is y = • A Vertical Line cuts through the x-axis, so the equation is x = y = 4 x = 3

  20. Equations of Horizontal and Vertical Lines: • Write the Equations of the Horizontal and Vertical line that goes through the point: • (3, 2) Horizontal: Vertical: • (4, 7) Horizontal: Vertical: • (2, 6) Horizontal: Vertical:

  21. Homework • pg 155 1-37all • Workbook 3.5 All Show all work on a separate sheet of paper

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