Question

Find the difference quotient of f(x)=5x+4

Answer 1

The differnce quotient is basically taking the derivitive (result will be f'(x)=5, but anyway)

here is the disffernce quotient
$lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h}$

so
for your equation
$lim_{h\rightarrow0}\frac{(5(x+h)+4)-(5x+4)}{h}$
$lim_{h\rightarrow0}\frac{5x+5h+4-5x-4}{h}$
$lim_{h\rightarrow0}\frac{5h}{h}$
h's cancel and you are left with 5
the differnce quotient is 5