#[A
linear function has the form][Una función lineal tiene la forma]#
$f(x) = mx + b\qquad$ \t
Notice that $f(0) = (m)(0) + b = b$, so
$b$ is the value of $f$ at $0$.
What about the term $m$? When $x=1$, we get $f(1) = (m)(1) + b = m+b$, so the value of $f$ has increased from $b$ to $m+b$; an increase of $m$. Similarly, when $x$ increases from $1$ to $2$, $f$ again increases by $m$; from $m+b$ to $2m + b$. In general,
$f(x)$ increases by $m$ units for every $1$-unit increase of $x$.
#[Examples][Ejemplos]#
Following is a table showing some values of $f(x) = 2x-1$.
Notice that the value at $x = 0$ is $b = -1$, and, as you go from left to right, the values of $y$ increase by by $m = 2$ for every 1-unit increase in $x.$