Average Rate of Change

The secant goes through 2 points. you need 2 points in order to get the slope

Tangent Line To Secant Formula

$y=mx+b$ $y=\frac{f(b)-f(a)}{b-a}(x-a)+f(a)$

Derivation

1. $m=\frac{f(b)-f(a)}{b-a}$
2. Remember that also $m=\frac{y-y_2}{x-x_2}$
   1. $y-y_2=m(x-x_2)$
   2. $y=m(x-x_2)+y_2$
   3. $y=\frac{f(b)-f(a)}{b-a}(x-a)+f(a)$

Negative & Positive Slope

Negative slope looks like this: Positive slope looks like this: