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8-5: Standard Form of an Equation of a Line

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8-5: Standard Form of an Equation of a Line

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  1. 8-5: Standard Form of an Equation of a Line Mr. Gallo

  2. Graphing Linear Functions Given the equation 3x + 2y = 6 Complete the table for the values of x and y:

  3. What do you notice about the coordinates when x = 0 and y = 0? ______________________Another name for the coordinate when x = 0 and the coordinate of the point is (0, y) is the _______________________Another name for the coordinate when y = 0 and the coordinate of the point is (x, 0) is the _______________________ Why are these points useful? • Graph the coordinates on the coordinate plane:

  4. The Slope Intercept Form Standard Form An equation of the form Ax + By = C is in standard form when: • A, B, and C are integers • A and B are not both zero, and • A is not negative.

  5. Example 1: Julia bought some CDs that cost $12 each and some DVD’s that cost $24 each for a total of $120. Write an equation in standard form that models this situation. Let x = the number of CDs Let y = the number of DVDs How would you represent the cost of x CDs? How would you represent the cost of y DVDs? Equation: _____________

  6. Write the equation that supports the data: Graph the equation on the coordinate system: Write the equation in standard form: Graph the equation on the coordinate system:

  7. Example 3 - Graph the equation What is the y-intercept? _______ What is the slope? ______ Example 4 - Graph the equation What is the y-intercept? ______ What is the slope? ______

  8. How are the graphs alike? ________________________________________________________________________ They have the same slopes. Parallel lines How are they different? ____________________________________________________________________ They have different y –intercepts.

  9. Example 6- Find the equation of the line passing through (0, 6) and with slope −4. Slope: _________. Substitute Point: Equation: _____________

  10. Example 7: Find the equation for the line passing through (3, −4) and (9, 0). Slope: _________. Substitute Point: Equation: _____________

  11. Homework: 8.3-8.4 Worksheet