Construct and interpret linear functions of the form y = mx + c to model practical situations, identifying the meaning of the gradient and intercept.

What this dot point is asking

You must be able to read a practical situation, set up a linear equation that fits it, explain what the gradient and intercept mean in context, and use the model to make predictions.

The linear model

A relationship is linear when $y$ changes by the same amount for each unit increase in $x$. The model is:

Building a model from words

The key is to identify the two parameters from the wording:

• A fixed starting amount, base fee, or initial value gives the intercept $c$.
• A "per unit" amount (per hour, per kilometre, per item) gives the gradient $m$.

Interpreting the model in context

Examiners reward interpretation, not just numbers. For the taxi model:

• The gradient $2.20$ means the fare increases by $2.20 for each extra kilometre.
• The intercept $4.50$ means the fare is $4.50 before any distance is travelled.

Predicting and the limits of a model

Substitute a value to predict. Predicting inside the range of your data is interpolation (usually reliable); predicting outside it is extrapolation (less reliable, because the linear pattern may not continue).