Equation of a Straight Line (Cambridge (CIE) A Level Maths): Revision Note

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

How do I find the equation of a straight line?

•  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

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

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

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

• 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