Find @FORMULA f(x)=-9x+8

$f (x) = - 9 x + 8$

Step 1

Consider the difference quotient formula.

$\frac{f (x + h) - f (x)}{h}$

Step 2

Find the components of the definition.

Evaluate the function at $x = x + h$ .

Replace the variable $x$ with $x + h$ in the expression.

$f (x + h) = - 9 (x + h) + 8$

Simplify the result.

Apply the distributive property.

$f (x + h) = - 9 x - 9 h + 8$

The final answer is $- 9 x - 9 h + 8$ .

$- 9 x - 9 h + 8$

Reorder $- 9 x$ and $- 9 h$ .

$- 9 h - 9 x + 8$

Find the components of the definition.

$f (x + h) = - 9 h - 9 x + 8$

$f (x) = - 9 x + 8$

$f (x + h) = - 9 h - 9 x + 8$

$f (x) = - 9 x + 8$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{- 9 h - 9 x + 8 - (- 9 x + 8)}{h}$

Step 4

Simplify.

Simplify the numerator.

Apply the distributive property.

$\frac{- 9 h - 9 x + 8 - (- 9 x) - 1 \cdot 8}{h}$

Multiply $- 9$ by $- 1$ .

$\frac{- 9 h - 9 x + 8 + 9 x - 1 \cdot 8}{h}$

Multiply $- 1$ by $8$ .

$\frac{- 9 h - 9 x + 8 + 9 x - 8}{h}$

Add $- 9 x$ and $9 x$ .

$\frac{- 9 h + 0 + 8 - 8}{h}$

Add $- 9 h$ and $0$ .

$\frac{- 9 h + 8 - 8}{h}$

Subtract $8$ from $8$ .

$\frac{- 9 h + 0}{h}$

Add $- 9 h$ and $0$ .

$\frac{- 9 h}{h}$

Divide $- 9$ by $1$ .

$- 9$

Step 5