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2.3 Slope and Rate of Change 9/10/2012

2.3 Slope and Rate of Change 9/10/2012. Vocabulary. Slope :. Is the ratio of the line’s vertical change (rise) to it’s horizontal change (run). rise. run. (x 1 , y 1 ) and (x 2 , y 2 ) are 2 points on the line. Find the slope of the line passing through and . (. (. ).

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2.3 Slope and Rate of Change 9/10/2012

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  1. 2.3Slope and Rate of Change9/10/2012

  2. Vocabulary Slope: Is the ratio of the line’s vertical change (rise) to it’s horizontal change (run). rise run (x1, y1) and (x2, y2) are 2 points on the line.

  3. Find the slope of the line passing through and . ( ( ) ) ( ( ) ) 5 5 3, 3, 2 2 ( ) ( ) x1,y1 x2,y2 SOLUTION – – 1, 1, Let and . = = y2y1 – Rise: Difference of y-values m = x2x1 – Run: Difference of x-values ( ) – 1 – 2 5 = Substitute values. – 3 – 3 3 – , or Simplify. = 4 4 Example 1 Find the Slope of a Line

  4. You can check that the result is the same if you let and . = = ( ) ( ) 5 3, 2 ( ) ( ) x1,y1 x2,y2 – 1, Example 1 Find the Slope of a Line By graphing:

  5. Classifying Lines by Slope y y y y positive zero negative x x x x undefined The line rises Vertical line The line falls Horizontal line

  6. ( ) ( ( ) ) 1 3, 3, 5 2 – – – 1, 4, 2 SOLUTION ( ) a. Because mis negative, the line falls. – 1. m = = = 3 ( ) – 4 – 3 5 2 which is undefined. Because mis undefined, the line is vertical. , b. m = = – 3 3 0 – – 2 1 – 3 – – 1 Example 2 Classify Lines Using Slope Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical. a. , b. ,

  7. Checkpoint ( ), ( ), 8 3, 2 – – – – – 1, 3 1 1, 2, ANSWER ( ( ) ) 1; rises 2. Find and Use Slope Find the slope of the line passing through the given points. Then tell whether the line rises, falls, is horizontal, or is vertical. 1. undefined slope; is vertical

  8. Checkpoint ( ( ), ) 4 4 ANSWER – – 5, 1, 3. 0; is horizontal Find and Use Slope Find the slope of the line passing through the given points. Then tell whether the line rises, falls, is horizontal, or is vertical.

  9. Example 3 ( ) – 1 m1 m2 > – Line 1: through and ( ) ( ) 2, 5 4, 1 Line 2: through and ( ) 4, 2 – ( ) 1, 6 – 6 Slope of line 1: m1 = = = – 3 2 – 2 6 4 – Slope of line 2: m2 = – = 4 2 – 4 5 – – 1 5 Compare Steepness of Lines Tell which line is steeper. SOLUTION Both lines have negative slope. Because , line 1 is steeper than line 2.

  10. Example 3 Compare Steepness of Lines By graphing: Line 1 is steeper than line 2.

  11. Checkpoint – ( ) ( ) 1, 5 3, 0 ( ) 2, 3 ANSWER line 1 5. Line 1: through and ( ( ) ) 21, 2 2, 27 – Line 2: through and ( ) 5, 5 – – ( ) 2, 6 Compare Steepness of Lines Tell which line is steeper. 4. Line 1: through and – Line 2: through and ( ) 4, 1 line 2

  12. Homework 2.3 p.82 #14-17, 21-26, 35-37 Remember: Copy the problems (except the graphs) Circle/Box final answer. Pencil Only.

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