Parallel lines Lines that are parallel have the same slope or gradient x y m1m1 m2m2 m 1 = m 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 m 1 = ¾ m 2 = ¾ y – y 1 = m(x – x 1 ) y – 5 = ¾(x + 3) 4y – 20 = 3x + 9 3x – 4y + 29 = 0 Notice both equations start with 3x – 4y
Perpendicular lines Lines that are perpendicular meet at 90°. The relationship we use is: To show lines are perpendicular we use: m 1 m 2 = –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.
Example 2 Show the lines 3x + 6y + 22 = 0 and y = 2x + 13 are perpendicular. 3x + 6y + 22 = 0 6y = –3x – 22 y = –½x – 3 2 / 3 m 1 = –½ y = 2x + 13 m 2 = 2 m 1 m 2 = –½ × 2 = –1 The lines are perpendicular
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 / 5 x + 3 m 1 = 3 / 5 y – y 1 = m(x – x 1 ) y – 4 = – 5 / 3 (x – 3) 3y – 12 = –5x x + 3y – 27 = 0
Today’s work Exercise 7.7 Page 291→292 Q1→4, 10 & 11
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