Watch out
Changing point order in only one part of the gradient fraction.
Scottish National 5 Mathematics
National 5 Maths Straight lines
Find gradients and equations of straight lines from points, gradients and equation forms.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Calculate the gradient in a consistent point order.
- Decide whether a calculator supports the method; exact working may still be required.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Straight lines is an assessed part of Scottish National 5 Mathematics in the algebra area. Find gradients and equations of straight lines from points, gradients and equation forms.
Calculate the gradient in a consistent point order.
Substitute one point into point-gradient form.
Rearrange to the requested form and check using the other point.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Visual support
Coordinate grid and gradient
Key formulae and rules
- m =
- y − b = m(x − a)
- y = mx + c
Check
Substitute a known point into each line equation; the coordinates should satisfy the equation exactly.
Exam tip
Keep equations aligned line by line so method marks remain visible, especially through sign and bracket changes.
Worked examples
Worked example 1
Straight lines worked example
Find the equation through (2, 5) and (6, 13).
- m = = 2
- y − 5 = 2(x − 2)
Answer: y = 2x + 1
Watch out
- Changing point order in only one part of the gradient fraction.
- Reading c as an x-intercept.