IB DP Maths: AI HL复习笔记2.1.1 Equations of a Straight Line

How do I find the gradient of a straight line?

• Find two points that the line passes through with coordinates (x₁, y₁) and (x₂, y₂)
• The gradient between these two points is calculated by

• • This is given in the formula booklet
• The gradient of a straight line measures its slope
  • A line with gradient 1 will go up 1 unit for every unit it goes to the right
  • A line with gradient -2 will go down two units for every unit it goes to the right

What are the equations of a straight line?How do I find an equation of a straight line?

• You will need the gradient
  • If you are given two points then first find the gradient
• It is easiest to start with the point-gradient form
  • then rearrange into whatever form is required
    • multiplying both sides by any denominators will get rid of fractions
• You can check your answer by using your GDC
  • Graph your answer and check it goes through the point(s)

How are the equations of parallel lines connected?

• Parallel lines are always equidistant meaning they never intersect
• Parallel lines have the same gradient
  • If the gradient of line l₁ is m₁ and gradient of line l₂ is m₂ then...
• • If they are equal then the lines are parallel

How are the equations of perpendicular lines connected?

• Perpendicular lines intersect at right angles
• The gradients of two perpendicular lines are negative reciprocals