Straight-line Equations and Functional Notation
Construct and interpret a straight-line equation and use functional notation accurately.
How to study National 5 Mathematics
Secure one operational skill at a time, connect it to neighbouring techniques, then apply it in unfamiliar contexts with complete working and a checked conclusion.
Core concepts
Concept 1
A line can be formed from a gradient and point using y − b = m(x − a), then simplified to an appropriate equivalent form.
Exam cue: Find or identify the gradient before substituting a known point.
Concept 2
Gradient and y-intercept can be identified from different equation forms after valid rearrangement.
Exam cue: Check that both given points satisfy the final line equation.
Concept 3
Functional notation f(x) names an output rule; evaluating f(a) means substituting a for every x.
Exam cue: Protect brackets when substituting negative values into a function.
Risk pitfalls and guardrails
Swapping x- and y-coordinate differences.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Using a point that is not on the line.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Treating f(x) as multiplication of f and x.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Memory anchors
Point–gradient form
y − b = m(x − a).
Gradient
Change in y divided by the corresponding change in x.
Intercept form
y = mx + c, where c is the y-intercept.
Line check
Substitute a known point into the final equation.
Function value
Replace every x in the rule with the stated input.
Negative input
Use brackets around the substituted negative number.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Which expression gives a line with gradient 2 and y-intercept −3?
A line has gradient 3 and passes through (1, 5). Which expression gives y in terms of x?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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