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Geometry

Learn about slopes, equations of lines, and line forms in Geometry. Practice examples included. Discover the different forms of equations and solve problems involving slopes and points on lines.

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Geometry

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  1. Geometry • Agenda 1. ENTRANCE 2. Go over Practice 3. 3-5 Lines in the Coordinate Plane 4. Practice 5. EXIT

  2. Practice

  3. Chapter 3 3-5 Lines in the Coordinate Plane

  4. Slope • The steepness of a line

  5. Types of Slope • Positive • Negative • Zero • No

  6. Equations of Lines • A line is a set of points. Every line has an equation that relates the coordinates of these points. ex: x + y = 5 (1, 4) (4, 1) (3, 2) (2, 3) (0, 5) (5, 0)

  7. Forms of a Line • These are each different forms of the same equation. x + y = 5 Standard form y = -x + 5 Slope-Intercept form y – 3 = -1(x -2) Point-Slope form

  8. Standard Form • This equation is of the form Ax + By = C. The x and y terms are on the left side and the constant is on the right side of the equation. x + y = 5

  9. Slope-Intercept Form • This equation is of the form y = mx + b. The y term is on the left and the x term is on the right side of the equation. The value of m is the slope of the equation. The value of b is the y-intercept. y = -x + 5

  10. Point-Slope Form • This equation is of the form y – y1 = m(x – x1). The y term is on the left and the x term is on the right side of the equation. The value of m is the slope of the equation. The values x1 and y1 are the coordinates of a point on the line. y – 3 = -1(x – 2) m = -1 (2, 3)

  11. Example #1 • Graph.

  12. Example #2 • Graph.

  13. Example #3 • Graph.

  14. Example #4 • Graph.

  15. Example #5 • Graph.

  16. Example #6 • Graph.

  17. Example #7 • Find the equation of a line with slope -8 that contains the point (3, -6).

  18. Example #8 • Find the equation of a line that contains the points (4, -9) and (-1, 1).

  19. Example #9 • Find the equation of a line with slope -1 that contains the point (2, -4).

  20. Example #10 • Find the equation of a line that contains the points (5, 0) and (7, -3).

  21. Example #11 • Find the equation of a horizontal line through the point (5, -1).

  22. Example #12 • Find the equation of a vertical line through the point (-7, -5).

  23. Example #13 • A wheelchair ramp is being constructed at a local hospital. What is the equation of the line that represents the ramp?

  24. Example #14 • The equation C = $0.50d + $0.75 represents the cost (C) for purchasing d number of donuts at the local bakery. • What is the slope of the line represented by this equation? • What does the slope represent in this situation? • What is the y-intercept of the line? • What does the y-intercept represent in this situation?

  25. Practice • WB 3-5 # 1, 2, 9, 11, 19, 25, 26, 33 • EXIT

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