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Parallel lines

y. m 1. m 2. x. Parallel lines. Lines that are parallel have the same slope or gradient.  m 1 = m 2. Example 1. What is the equation of the line parallel to 3 x – 4y + 22 = 0, through the point ( –3, 5)?. 3 x – 4y + 22 = 0 4y = 3 x + 22

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Parallel lines

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  1. y m1 m2 x Parallel lines Lines that are parallel have the same slope or gradient m1 = m2

  2. Example 1 What is the equation of the line parallel to 3x – 4y + 22 = 0, through the point (–3, 5)? 3x – 4y + 22 = 0 4y = 3x + 22 y = ¾x + 5½  m1 = ¾  m2 = ¾ y – y1 = m(x – x1) y – 5 = ¾(x + 3) 4y – 20 = 3x + 9 3x – 4y + 29 = 0 Notice both equations start with 3x – 4y

  3. Perpendicular lines Lines that are perpendicular meet at 90°. The relationship we use is: To show lines are perpendicular we use: m1m2 = –1 If we know the lines are perpendicular and need the second gradient we use: Another way of thinking about this is the second gradient is the negative reciprocal of the first.

  4. Example 2 Show the lines 3x + 6y + 22 = 0 and y = 2x + 13 are perpendicular. 3x + 6y + 22 = 0 6y = –3x – 22 y = –½x – 32/3 m1 = –½ y = 2x + 13 m2 = 2 m1m2 = –½ × 2 = –1 The lines are perpendicular

  5. Example 3 Find the equation of the line that is perpendicular to 3x – 5y + 15 = 0 passes through the point (3, 4). 3x – 5y + 15 = 0 5y = 3x + 15 y = 3/5x + 3 m1 = 3/5 y – y1 = m(x – x1) y – 4 = –5/3(x – 3) 3y – 12 = –5x + 15 5x + 3y – 27 = 0

  6. Today’s work Exercise 7.7 Page 291→292 Q1→4, 10 & 11

  7. Yesterday’s work Exercise 7.5 Page 283 Q1, 4, 7… Exercise 7.6 Page 287 Q1 a, b, e & g Q2 Q3 a & c Q5 Q9

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