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