Linear function
|
|
A linear function is a mathematical function term of the form:
- f(x) = m x + c
where m and c are constants.
This function can also be written
- y = m x + c
and plotted on an x,y graph. It forms a straight line, as the name implies.
The constant m is often called the slope or gradient while c is the y-intercept, which gives the point of intersection between the graph of the function and the y-axis.
Examples:
- f(x)= 2x + 1
(here m=2, c=1)
- f(x) = x
(m=1, c=0)
- f(x)= 9 x - 2
- f(x)= -3 x + 4
On a line graph, changing m makes the line steeper or shallower, and changing c moves the line up or down.
As mentioned, the line crosses the y-axis at the co-ordinate (0,c). It crosses the x-axis at (-c / m) (solving for 0 = m x + c we get x = -c / m).de:Lineare Funktion ja:一次関数 nl:Lineaire functie pl:Funkcja liniowa sl:Linearna funkcija