2.1.3 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