We need to find the equation of a line that passes through the point $(4, 5)$ and is parallel to the line $y = x - 1$.

1. Problem Description

We need to find the equation of a line that passes through the point $(4, 5)$ and is parallel to the line $y = x - 1$.

2. Solution Steps

Two parallel lines have the same slope. The given line is $y = x - 1$, which is in slope-intercept form $y = mx + b$. The slope of this line is $m = 1$.

Therefore, the line we are looking for also has a slope of $1$.

Using the point-slope form of a line, $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is the given point and $m$ is the slope, we can plug in the values $x_1 = 4$, $y_1 = 5$, and $m = 1$:

$y - 5 = 1(x - 4)$

$y - 5 = x - 4$

$y = x - 4 + 5$

$y = x + 1$

3. Final Answer

The equation of the line is $y = x + 1$.

The correct answer is (b).