Applying straight line graphs to solve problems

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)

New NZC (2026)

Alpha textbook: Check Your Understanding, pg 201 – 203
Alpha textbook: Extension Learning Objectives
Dr Austin Maths - Plotting Straight Lines and Finding Areas and Perimeters Practice GridQuestions PDF · Answers
Dr Austin Maths - Conversion Graphs Practice GridQuestions PDF · Answers

{'term': 'Linear relationship', 'definition': 'A relationship between two variables that can be represented by a straight-line graph'}
{'term': 'Equation model', 'definition': 'An algebraic equation that represents a real-world situation'}
{'term': 'Gradient', 'definition': 'The slope of the line, representing the rate of change'}
{'term': 'Y-intercept', 'definition': 'The starting value or constant term in the equation $y = mx + c$'}
{'term': 'Substitution', 'definition': 'Replacing variables with specific numerical values in an equation'}
{'term': 'Context', 'definition': 'The real-world situation that the equation describes'}

Read and interpolate values from straight-line models, including conversion graphs.
Interpret the gradient of a straight-line graph as a rate of change in the context of the problem.
Interpret the y-intercept of a straight-line graph as a starting value or fixed charge in the context of the problem.
Use a straight-line graph to interpolate a value that lies within the plotted range.
Use a straight-line graph to extrapolate a value beyond the plotted range, recognising the extra uncertainty and checking the physical domain.
Compare contextual lines graphically and justify a decision from their relative positions and crossing point.
Read vertices formed by straight-line boundaries and calculate the enclosed shape's area or perimeter without algebraically solving simultaneous equations.