Linear Functions

≈ 25 min

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Linear Functions

In $f(x)=mx+c$ , $m$ sets gradient and $c$ the vertical intercept. Two points determine a non-vertical line. At Grade 10, fluent symbolic work must stay connected to graphs, tables, diagrams and real quantities.

Worked reasoning

Gradient is $(8-2)/(3-0)=2$ .
The $y$ -intercept is 2, so $y=2x+2$ .

Key idea

Two points determine a non-vertical line.

Find the line through $(0,2)$ and $(3,8)$ .

Which statement best captures the central mathematical idea in Linear Functions?

Two points determine a non-vertical line.

A memorised rule may be used without checking signs, domains, units, graph family or geometric hypotheses.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about Linear Functions, which move is most reliable?

Identify the mathematical family, list the given quantities and state the domain or geometric conditions for linear functions.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with Linear Functions?

A memorised rule may be used without checking signs, domains, units, graph family or geometric hypotheses.

Two points determine a non-vertical line.

Identify the mathematical family, list the given quantities and state the domain or geometric conditions for linear functions.

Use substitution, a second representation or a magnitude estimate to verify the result.

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