Straight line graphs

• y = mx + c


  Equation of a straight line, where m is the gradient and c is the y-intercept

  
• Finding the gradient m of a straight line


  1. Take two random points A (x1, y1) and B (x2, y2) on the line

  2. Calculate the horizontal and vertical distance between the points

  3. Use the formula m = (y2 - y1) / (x2 - x1)

  
• Straight line equations


  • y = mx + c, where m is the gradient and c is the y-intercept
  • ax + by + c = 0, where a, b, and c are real numbers

  
• Equation of a straight line using a point and gradient


  y - y1 = m(x - x1)

  
• Parallel lines


  Have the same gradient
• Perpendicular lines


  Are normal to each other, intersecting at right angles

  
• Length and area


  Can be calculated using Pythagoras theorem
• The lines y = 2x + 2 and y = 2x are parallel as they have the same gradient m = 2

  
• The lines y = -(1/2)x + 2 and y = 2x are perpendicular

  
• Calculating the distance d between two points A and B


  d = √((x2 - x1)^2 + (y2 - y1)^2)