Linear functions

Lines. A line may be determined by a slope $m$ and a $y$-intercept $b$. If so, the equation of the line can be written by

$\displaystyle y = m x + b.
$

General form of a line. A line is ``always'' expressed in the form of a linear equation

$\displaystyle a x + b y = c.$ (1)

\includegraphics{lec01b.ps}

Linear functions. A function $f$ is called a linear function if

$\displaystyle f(x) = a x + b$ (2)

with slope $a$ and intercept $b$. A linear function $f$ represents a line, but not always otherwise; compare (2) with (1).



Department of Mathematics
Last modified: 2005-09-29