Sketching Straight LinesUsing x & y intercepts  C cannot be equal to 0  Gradient  intercept method  ax + by = c > e.g 2x  5y = 10  y = mx + c  y = 0 when solving x  Horizontal Line  2x  0 = 10  gradient = 0  x = 5  y = c  x = 0 when solving y  Vertical Line  2(0)  5y = 10  gradient = undefined  5y = 10  x = a  y = 10/5  a > xintercept  y = 2 
  Finding the equation of a straight lineGradient + yintercept  Gradient + a point (x1, y1)  2 points (x1, y1) (x2, y2)  Distance between 2 points  Sub into equation  Sub into equation  1st find m  Sub into equation  y = mx + c  y  y1 = m(x  x1)  m = y2  y1/x2  x1  AB = √(x2  x1)² + (y2  y1)²  Example  Example  2nd sub into equation  Example  c = 5  m = 1  m = 2  (2, 0.5)  y  y1 = m(x  x1)  A = (3, 5)  B = (2, 1)  y = 1x + 5  y + 0.5 = 2(x  2)  Example  AB = √(2  3)² + (1  5)²   y + 0.5 = 2x  4  (1, 4) , (5, 2)  AB = √(5)² + 6²   y = 2x  4.5  m = 2  4/3  (1)  AB = √25 + 36    m = 2/4 > 1/2  AB = √61    y  4 = 1/2(x   1)    y  4 =  1/2x  1/2    y =  1/2x + 7/2 
  Middle point of a lineMiddle point of a line  Paralell Lines  Perpendicular Lines  Sub into equation  i.e / means divide  Sub into equation  Sub into equation  M = (x1 + x2/2, y1 + y2/2)  m1 = m2  m1 x m2 = 1 or m2 = 1/m1  Example  Example  1st find m (gradient)  Example  1st find m (gradient)  (3, 5)  (2, 7)  A (4, 13)  B (2, 9)  A (4, 9)  B (2, 6)  M = 3 + 2/2, 5 + 7/2  mAB = 9  13/2  4  mAB = 6  9/2  (4)  M = (5/2, 12/2)  mAB = 4/2  mAB = 15/6  M = (5/2, 6)  mAB = 2  mAB = 5/2   C (0, 10)  D (15, 0)  C (5, 8)  D (10, 14)   mCD = 0  (10)/15  0  mCD = 14  8/10  (5)   mCD = 10/15  mCD = 6/15   mCD = 2/3  mCD = 2/5   ∵ mAB ≠ mCB  2nd  sub into m1 x m2 = 1   ∴ not parralell  5/2 x 2/5 = 1    10/10 = 1    ∴ AB ⊥ CD 

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