Find the Difference Quotient f(x)=-6x+5

$f (x) = - 6 x + 5$

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.

$f (x + h) = - 6 (x + h) + 5$

Simplify the result.

Apply the distributive property.

$f (x + h) = - 6 x - 6 h + 5$

The final answer is $- 6 x - 6 h + 5$ .

$- 6 x - 6 h + 5$

Reorder $- 6 x$ and $- 6 h$ .

$- 6 h - 6 x + 5$

Find the components of the definition.

$f (x + h) = - 6 h - 6 x + 5$

$f (x) = - 6 x + 5$

$f (x + h) = - 6 h - 6 x + 5$

$f (x) = - 6 x + 5$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{- 6 h - 6 x + 5 - (- 6 x + 5)}{h}$

Step 4

Simplify.

Simplify the numerator.

Apply the distributive property.

$\frac{- 6 h - 6 x + 5 - (- 6 x) - 1 \cdot 5}{h}$

Multiply $- 6$ by $- 1$ .

$\frac{- 6 h - 6 x + 5 + 6 x - 1 \cdot 5}{h}$

Multiply $- 1$ by $5$ .

$\frac{- 6 h - 6 x + 5 + 6 x - 5}{h}$

Add $- 6 x$ and $6 x$ .

$\frac{- 6 h + 0 + 5 - 5}{h}$

Add $- 6 h$ and $0$ .

$\frac{- 6 h + 5 - 5}{h}$

Subtract $5$ from $5$ .

$\frac{- 6 h + 0}{h}$

Add $- 6 h$ and $0$ .

$\frac{- 6 h}{h}$

Divide $- 6$ by $1$ .

$- 6$

Step 5