Find the Difference Quotient f(x)=-5x+8

$f (x) = - 5 x + 8$

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.

$f (x + h) = - 5 (x + h) + 8$

Simplify the result.

Apply the distributive property.

$f (x + h) = - 5 x - 5 h + 8$

The final answer is $- 5 x - 5 h + 8$ .

$- 5 x - 5 h + 8$

Reorder $- 5 x$ and $- 5 h$ .

$- 5 h - 5 x + 8$

Find the components of the definition.

$f (x + h) = - 5 h - 5 x + 8$

$f (x) = - 5 x + 8$

$f (x + h) = - 5 h - 5 x + 8$

$f (x) = - 5 x + 8$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{- 5 h - 5 x + 8 - (- 5 x + 8)}{h}$

Step 4

Simplify.

Simplify the numerator.

Apply the distributive property.

$\frac{- 5 h - 5 x + 8 - (- 5 x) - 1 \cdot 8}{h}$

Multiply $- 5$ by $- 1$ .

$\frac{- 5 h - 5 x + 8 + 5 x - 1 \cdot 8}{h}$

Multiply $- 1$ by $8$ .

$\frac{- 5 h - 5 x + 8 + 5 x - 8}{h}$

Add $- 5 x$ and $5 x$ .

$\frac{- 5 h + 0 + 8 - 8}{h}$

Add $- 5 h$ and $0$ .

$\frac{- 5 h + 8 - 8}{h}$

Subtract $8$ from $8$ .

$\frac{- 5 h + 0}{h}$

Add $- 5 h$ and $0$ .

$\frac{- 5 h}{h}$

Divide $- 5$ by $1$ .

$- 5$

Step 5