Worked example 1
Find a line equation
Find the equation of the line through (2, 5) with gradient 3.
- Use y − b = m(x − a).
- Substitute m = 3 and (a, b) = (2, 5)
- Expand if required.
Answer: y − 5 = 3(x − 2), so y = 3x − 1
Higher Mathematics
Higher Maths Straight line methods
Practise straight line methods for Scottish Higher Mathematics with worked examples, clear methods and original interactive questions. Find gradients and equations, including parallel and perpendicular lines and m = tan θ.
Before you start
- Subtract coordinates in a consistent order.
- Know y = mx + c and y − b = m(x − a)
- Recall that perpendicular gradients multiply to −1.
Explanation
Straight-line work is the language used across coordinate geometry, tangents and normals. The gradient tells you steepness and direction; the equation fixes the line in the plane.
At Higher, line questions often combine coordinate facts with parallel or perpendicular relationships.
Method and rules
- m =
- y = mx + c
- Through (a, b): y − b = m(x − a)
- Parallel lines have equal gradients; perpendicular gradients are negative reciprocals.
Worked examples
Worked example 2
Use perpendicular gradients
A line has gradient 4. Find the gradient of a perpendicular line.
- Take the negative reciprocal.
- Change the sign and flip the fraction.
So: The perpendicular gradient is −.
Watch out
- Swapping x-change and y-change in the gradient formula.
- Subtracting coordinates in different orders.
- Using the same gradient for a perpendicular line.
- Losing the sign when finding c.
Exam reminder
Leave line equations in the requested form. If no form is specified, a clear equation such as y = mx + c is acceptable.
Related Higher Maths topics
Continue with the methods that connect most closely to this topic.