Answer
$y = x - 3$
Work Step by Step
1. Find the derivative of the function $f(x)$
$f(x) = e^{x-4}$
$f'(x) = 1e^{x-4}$
$f'(x) = e^{x-4}$
2. Substitute the coordinates $(4,1)$ to find the slope of the tangent
$f'(4) = e^{(4-4}$
$m = e^{0}$
$m = 1$
3. Substitute the slope into the equation of the tangent to find $b$
$y = mx + b$
$1 = 1(4) + b$
$1 = 4 + b$
$b = -3$
4. Write the equation of the tangent
$y = x - 3$
