# Lines and linear relationships

*function*which inputs a value \(\normalsize{x}\), and outputs another value \(\normalsize{y}\). To emphasize this functional aspect, it is common to also introduce a specific name of the function in question, say \(\normalsize{f}\). Thus we would write \[\Large{y=f(x)=-2x+4}\]and sometimes we dispense with the reference to \(\normalsize{y}\), so writing \(\normalsize{f(x)=-2x+4}\).For example you can verify that \(\normalsize{f(0)=4}\), \(\normalsize{f(1)=2}\), \(\normalsize{f(10)=-16}\) and \(\normalsize{f(-3)=10}\).Any function of the form \(\normalsize{f(x)=ax+b}\) for fixed \(\normalsize{a,\;b}\) is called a

*linear function*provided \({\normalsize a \neq 0}\). We say that the physical line on the page for \(\normalsize{y=ax+b}\) is the

*graph*of that function.The line \(\normalsize x=0\) is

*not*a function. This is because when \(x=0\) there are too many possible values for \(\normalsize y\). In this case we use a more general term, and call \(\normalsize x=0\) a

*relation*.

#### Maths for Humans: Linear, Quadratic & Inverse Relations

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