A linear function is a polynomial of degree \(1\) or \(0\), i.e. a function \(f:\mathbb R\to\mathbb R\) of the form \[f(x):=a_1x+a_0,\quad\quad a_0,a_1\in\mathbb R.\]
In the following interactive figure, you can drag the sliders to manipulate the values of the coefficients \(a_0,a_1\) and see the behavior of resulting linear function. The initial values are(when the Reset button is pressed) are set to \(0\).
Proofs: 2 3
Propositions: 4 5