derivative

$f'(x) = lim_{h->0} \frac{f(x+h)-f(x)}{h}$

$g'(x) = lim_{x->t} \frac{g(x)-f(t)}{x-t}$ same as . $g'(x)=lim_{x->t}\frac{g(t-h)-g(t)}{h}$

Slope Forms

1. Point Slope Form: $y-y_1 = m(x-x_1)$

2. Slope Intercept Form: $y = mx + b$

3. Standard Form: $Ax + By = C$

m describes the slope, b describes the y-intercept

Example: (-3, 6)(6, 0)

$m => \frac{0-6}{6-(-3)} = -\frac{6}{9} = -\frac{2}{3}$

1. $y-6 = -\frac{2}{3}(x+3)$

2. $y-6 = -\frac{2}{3}x-2 => y = -\frac{2}{3}x + 4$

3. $\frac{2}{3}x + y = 4$