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3.4 Find and Use Slopes of Lines

3.4 Find and Use Slopes of Lines. Define the following words: Slope Rise Run. - The rate of change. - The change in y. - The change in x. Key Concept: Slope of lines in the Coordinate Plane. Negative slope: falls from left to right Positive slope: rises from left to right

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3.4 Find and Use Slopes of Lines

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  1. 3.4 Find and Use Slopes of Lines Define the following words: Slope Rise Run - The rate of change - The change in y - The change in x

  2. Key Concept: Slope of lines in the Coordinate Plane • Negative slope: falls from left to right • Positive slope: rises from left to right • Zero slope – horizontal • Undefined slope: vertical

  3. Find the slope of line aand line d. – 1 = = = = 2 4 = = = – 2 0 y2 – y1 y2 – y1 4 – 0 4 – 2 x2 – x1 x2 – x1 6 – 8 6 – 6 EXAMPLE 1 Find slopes of lines in a coordinate plane SOLUTION Slope of linea:m Slope of lined:m which is undefined.

  4. Postulate 17: Slopes of Parallel Lines • In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope. m || n

  5. Find the slope of each line. Which lines are parallel? m1 4 = = = – 4 – 1 0 – 4 – 4 1 – 5 4 m2 = = = – 1 – 3 – (– 2 ) 3 – 4 EXAMPLE 2 Identify parallel lines SOLUTION Find the slope ofk1through (– 2, 4) and (– 3, 0). Find the slope of k2through (4, 5) and (1, 3).

  6. – 5 – 2 – 3 5 m3 = = = – 1 5 – 6 EXAMPLE 2 Identify parallel lines Find the slope of k3through (6, 3) and (5, – 2). Compare the slopes. Because k1and k2have the same slope, they are parallel. The slope of k3is different, so k3is not parallel to the other lines.

  7. Postulate 18: Slopes of Perpendicular Lines In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1.

  8. Line hpasses through (3, 0) and (7, 6). Graph the line perpendicular to h that passes through the point (2, 5). STEP 1 Find the slope m1of line h through (3, 0) and (7, 6). 3 6 m1 = = = 6 – 0 2 4 7 – 3 EXAMPLE 3 Draw a perpendicular line SOLUTION

  9. STEP 2 Find the slope m2of a line perpendicular to h. Use the fact that the product of the slopes of two perpendicular lines is –1. m2 – 1 = m2 – 2 = Multiply each side by 3 STEP 3 3 2 2 Use the rise and run to graph the line. 3 EXAMPLE 3 Draw a perpendicular line Slopes of perpendicular lines

  10. ANSWER The correct answer is D. EXAMPLE 4 Standardized Test Practice SOLUTION The rate at which the skydiver descended is represented by the slope of the segments. The segments that have the same slope are aand c.

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