given the function f(x)=8 - 7x, find the difference quotient (f(a + h)-f(a))/h. (f(a + h)-f(a))/h =

Explanation:

Step1: Find $f(a + h)$

Substitute $x=a + h$ into $f(x)$: $f(a + h)=8-7(a + h)=8-7a-7h$.

Step2: Find $f(a)$

Substitute $x = a$ into $f(x)$: $f(a)=8-7a$.

Step3: Calculate $f(a + h)-f(a)$

$(8-7a - 7h)-(8 - 7a)=8-7a-7h - 8 + 7a=-7h$.

Step4: Calculate the difference - quotient

$\frac{f(a + h)-f(a)}{h}=\frac{-7h}{h}=-7$.

Answer:

$-7$