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
- c is the y-axis intercept
- An 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 Gradients - Parallel and Perpendicular Gradients
- Using Tangents and Normals - Differentiation
- see Tangents & Normals
- Other ways
- Collinear lines are the same straight line so gradients are equal
- Angle facts and circle theorems
e.g. a radius and tangent are perpendicular