Linear Graphs (CIE IGCSE Additional Maths)

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

• 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?

• 
  • This is the gradient-intercept form
  • It clearly shows the gradient m and the y-intercept (0, c)
• 
• • This is the point-gradient form
  • It clearly shows the gradient m and a point on the line (x₁, y₁)
• 
  • This is the general form
  • You can quickly get the x-intercept and y-intercept

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

How do I find the midpoint of a line (segment)?

• The midpoint of a line will be the same distance from both endpoints
• You can think of a midpoint as being the average (mean) of two coordinates
• The midpoint of  and is

• M is often used as the midpoint between two points (x₁, y₁) (x₂, y₂)
• It is the average of both the x and y coordinates

How do I calculate the length of a line?

• The distance between two points with coordinates  and  can be found using the formula

• This formula is really just Pythagoras’ Theorem  , applied to the difference in the -coordinates and the difference in the -coordinates;

• You may be asked to find the length of a diagonal in 3D space
  • This can be answered using 3D Pythagoras