Equation of a Straight Line (Edexcel IAL Maths)

Spec point — 2.1

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 rearranged 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

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

• 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

Exam Hint

• 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