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?
- Two points on a line
- Parallel or perpendicular to another line (see Parallel and Perpendicular Gradients)
- 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 theoremseg. a radius and tangent are perpendicular
Exam 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
