Slope

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Slope

  1. 1. 12-5 Slope Warm Up Problem of the Day Lesson PresentationCourse 2
  2. 2. 12-5 Slope Learn to determine the slope of a line and to graph a line, given one point, the y-intercept, and the slope.Course 2
  3. 3. 12-5 Slope Lesson Title Here Insert Vocabulary slope y-intercept slope-intercept formCourse 2
  4. 4. 12-5 Slope The slope of a line is a measure of its steepness and is the ratio of rise to run: y Run Rise x y-intercept The y-coordinate of the point where a line crosses the y-axis is called the y-intercept.Course 2
  5. 5. 12-5 Slope Additional Example 1A: Identifying Slope and y-intercept of a line A. Give the slope and y-intercept of the line. 3 3 y-intercept The rise is 3. The run is 3. slope = rise = 3 = 1 run 3 The y-intercept is –4.Course 2
  6. 6. 12-5 Slope Additional Example 1B: Identifying the Slope and y-intercept of a Line B. Give the slope and y-intercept of the line. y-intercept 2 The rise is 0. The run is 2. slope = rise = 0 = 0 run 2 The y-intercept is –1.Course 2
  7. 7. 12-5 Insert Lesson Title Here Slope Try This: Example 1A A. Give the slope and y-intercept of the line. The rise is 0. The run is –8. y-intercept slope = rise = 0 = 0 run –8 The y-intercept is –3. –8(–4, –3) (4, –3)Course 2
  8. 8. 12-5 Insert Lesson Title Here Slope Try This: Example 1B B. Give the slope and y-intercept of the line. (–2, 4) –4 The rise is 8. The run is –4. 8 y-intercept slope = rise = 8 = –2 run –4 The y-intercept is 0. (0, –4)Course 2
  9. 9. 12-5 Slope A linear equation with the variable y isolated on the left-hand side of the equation is in slope-intercept form. y = mx + b Slope y-interceptCourse 2
  10. 10. 12-5 Slope Additional Example 2: Identifying Slope and y-intercept in a Linear Equation Give the slope and y-intercept of each line, given the equation. A. y = 3x – 1 y = 3x – 1 The slope is 3. The y-intercept is –1. B. y = 1 x + 2 2 y = 1x + 2 2 1. The slope is 2 The y-intercept is 2.Course 2
  11. 11. 12-5 Insert Lesson Title Here Slope Try This: Example 2 Give the slope and y-intercept of each line, given the equation. A. y = 4x – 4 y = 4x – 4 The slope is 4. The y-intercept is –4. 1 B. y = 3 x + 3 y = 1x + 3 3 1. The slope is 3 The y-intercept is 3.Course 2
  12. 12. 12-5 Slope When you know the slope and any one point on a line, you can graph the line.Course 2
  13. 13. 12-5 Slope Additional Example 3: Graphing Linear Equations Using Slope and y-intercept Graph each line, given the equation. A. y = –2x + 1 y = –2x + 1 (–1, 3) 2 The slope is –2 or –1 The y-intercept is 1. From point (0, 1) move 2 units up (rise) and 1 unit left (run) to find another point on the line. Draw a line to connect the pointsCourse 2
  14. 14. 12-5 Slope Additional Example 3B: Graphing Linear Equations Using Slope and y-intercept Graph the line, given the equation. B. y = 3 y = 0x + 3 (0, 3) The slope is 0. The y- intercept is 3. Locate the point (0, 3). When the slope is zero the line is horizontal. Draw a horizontal line through point (0, 3).Course 2
  15. 15. 12-5 Insert Lesson Title Here Slope Try This: Example 3A Graph the line, given the equation. A. y = x – 4 y = 1x – 4 The slope is 1. The y-intercept is –4. From point (0, –4) move 1 unit up (rise) and 1 unit right (run) to find another (1, –3) point on the line. Draw a (0, –4) line to connect the pointsCourse 2
  16. 16. 12-5 Insert Lesson Title Here Slope Try This: Example 3B Graph the line, given the equation. B. y = –1 y = 0x – 1 The slope is 0. The y- intercept is –1. Locate the point (0, –1). (–3, –1) (0, –1) When the slope is zero the line is horizontal. Draw a horizontal line through point (0, –1).Course 2
  17. 17. 12-5 Slope Lesson Title Here Insert Lesson Quiz: Part 1 Tell the slope and y-intercept of each line, given the equation. 1. y = x – 5 1; –5 2. y = 3 x 3 ; 0 4 4 3. y = –2x + 7 –2; 7Course 2
  18. 18. 12-5 Slope Lesson Title Here Insert Lesson Quiz: Part 2 4. Graph the line, given the equation y = 1x – 2. 2Course 2

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