Scattergraphs and Linear Models
Form a sensible best-fitting line model and use interpolation or cautious extrapolation to estimate an output.
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 best-fitting straight line represents an approximate linear pattern rather than passing through every point.
Exam cue: Choose two well-separated points on the fitted line.
Concept 2
Two suitable points on the fitted line determine its gradient and equation; they do not need to be original data points.
Exam cue: Form the equation and check it follows the visible direction and scale.
Concept 3
Substitution estimates y for a given x, but reliability depends on scatter and whether the estimate is inside the observed range.
Exam cue: Label interpolation as safer than extrapolation when appropriate.
Risk pitfalls and guardrails
Joining the first and last observed points automatically.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Using two raw points not on the line of best fit.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Presenting an extrapolation as exact.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Memory anchors
Best-fitting line
A straight model balancing the scatter rather than joining every point.
Model gradient
Use two well-separated points on the fitted line.
Model equation
y = mx + c.
Estimate y
Substitute the given x into the fitted-line equation.
Interpolation
Estimate within the observed x-range.
Extrapolation
Estimate beyond the observed range and treat it cautiously.
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
Two well-separated points on a fitted line are (2, 5) and (8, 17). Which expression gives the line?
A fitted line passes through (10, 24) and (30, 54). Find its equation.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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