---
abstract: How I enriched a non-interesting activity of proportionality
author: Xavier Bordoy
comments: 'True'
created: '20200226173831913'
date: '2016-05-30'
keywords:
- línies
- representació gràfica
- funció afí
- funcions
- bitàcola
lang: en
license: CC-BY 4.0
modified: '2020-02-26'
title: Only when you need
type: text/x-markdown
---
I posed this problem in class:
> In a certain city, gas service is paying 15 € fixed a month and 0.75 € for each cubic meter consumed.
>
> a. How much do you pay for $3 m^3$? And for $5 m^3$
> a. Plot the function which relates consumed cubic meters and the cost of the service
When do you need the formula of the relation there? Clearly you could get (a) without a formula. And you could plot the points using value table (with previosly calculated values in (a) if you want) but you *need* the formula of the relation ($cost = 15 + 0.75 meter$) for *assuring* that you could join the points with a straight line (using the theoric fact that: afine functions correspond to straight lines). Otherwise you would not know if the plot is a straight line or a curve.
My students understood more clearly the connection between plots and functions when I ask them for which step needs here the formula.