Equation of a Straight Line (CIE A Level Maths: Pure 1)

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Equation of a Straight Line

What is the equation of a straight line?

  • y = mx + c is the equation for any straight line
  • m is gradient given by “difference in y” ÷ “difference in x” or dy/dx
  • c is the y-axis intercept
  • Alternative form is ax + by + c = 0 where a, b and c are integers

 

Equation of a Straight Line Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

How do I find the equation of a straight line?

Equation of a Straight Line Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes

  •  Two features of a straight line are needed
    • gradient, m
    • a point the line passes through, (x1, y1)
  • The equation can then be found using y – y1 = m(x - x1)
  • This can be arranged into either y = mx + c or ax +by + c = 0

Equation of a Straight Line Notes Diagram 6, A Level & AS Level Pure Maths Revision Notes 

How do I find the gradient of a straight line?

  • There are lots of ways to find the gradient of a line

  • Using two points on a line to find the change in y divided by change in x

bold italic m bold equals fraction numerator bold y subscript bold 2 bold minus bold y subscript bold 1 over denominator bold x subscript bold 2 bold minus bold x subscript bold 1 end fraction

Equation of a Straight Line Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes  

  • Using the fact that lines are parallel or perpendicular to another line (see Parallel and Perpendicular Gradients)

 Equation of a Straight Line Notes Diagram 4, A Level & AS Level Pure Maths Revision Notes 

  • Using Tangents and Normals - Differentiation (see Gradients, Tangents & Normals)

 

Equation of a Straight Line Notes Diagram 5, A Level & AS Level Pure Maths Revision Notes

 

  • Other ways
    • Collinear lines are the same straight line so gradients are equal
    • Angle facts and circle theorems

      eg. a radius and tangent are perpendicular

Examiner Tip

  • Working with straight lines can involve lots of algebra, but sketching a diagram will always help.
  • Use a sketch to check if answers seem about right.

Worked example

Equation of a Straight Line Example Diagram, A Level & AS Level Pure Maths Revision Notes

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.