# What is the slope of the line normal to the tangent line of f(x) = 2x-2  at  x= 3 ?

May 8, 2018

$\text{Slope} = 2$

#### Explanation:

A graph of $y = f \left(x\right) = m x + c$ will always have a gradient of $m$.

So, when we have $f \left(x\right) = 2 x - 2$, the gradient is always $2$

This can be shown by differentiation:

$f \left(x\right) = 2 x - 2 = 2 {x}^{1} - 2 {x}^{0}$

$f ' \left(x\right) = 1 \cdot 2 {x}^{1 - 1} - 0 \cdot 2 {x}^{0 - 1} = 2 {x}^{0} - 0 = 2$