Linear function

A linear function $f(x)=ax+b$ has a graph that is a straight line. The slope $a$ is the change in $y$ per change in $x$ , and $b$ is the y-intercept.

f(x) = ax + b

linear function

a = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\Delta y}{\Delta x}

slope between two points

Symbols

$a$	slope
$b$	y-intercept (where $x=0$ )

The line through $(1,3)$ and $(4,12)$ : $a = \frac{12-3}{4-1}=3$ , and $3 = 3\cdot 1+b \Rightarrow b=0$ , so $f(x)=3x$ .

It is

a

, not

b

, that is the slope - easy to mix up.