## Definition

It's called ** polynomial function of the 1st degree**, or ** similar function**, to any function *f *IR to IR given by a law of the form f (*x*) = a*x* + b where a and b are given real numbers and a0.

In function f (*x*) = a*x* + b, the number ** The** is called the coefficient of *x* is the number ** B** It is called constant term.

Here are some examples of 1st degree polynomial functions:

f (*x*) = 5

*x*- 3, where a = 5 and b = - 3

f (

*x*) = -2

*x*- 7, where a = -2 and b = - 7

f (

*x*) = 11

*x*where a = 11 and b = 0

# Graphic

The graph of a polynomial function of the 1st degree, *y* = a*x* + b, with a0, is an oblique line to the axes O*x* it's the*y*. For example, let's build the graph of the function *y* = 3*x* - 1:

As the graph is a straight line, just get two of its points and connect them with the help of a ruler:

a) To *x* = 0, we have *y* = 3 · 0 - 1 = -1; therefore, a point is (0, -1).

b) To *y* = 0, we have 0 = 3*x* - 1; therefore, and another point is .

We mark the points (0, -1) and in the Cartesian plane and connect the two with a straight line.

x | y |

0 | -1 |

0 |

We have already seen that the graph of the related function *y* = a*x* + b is a straight line.

The coefficient of *x*, **The**, is called ** angular coefficient of the line** and, as we shall see, it is linked to the slope of the line with respect to the O axis*x*.

The constant term, **B**, is called the linear coefficient of the line. For x = 0, we have *y* = a · 0 + b = b. Thus, the linear coefficient is the ordinate of the point at which the line cuts the O axis.*y*.