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

1. Problem Description

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

2. Solution Steps

If two lines are parallel, they have the same slope. The given line is $y = x - 1$, which has a slope of $1$. Therefore, the line we are looking for also has a slope of $1$.

The equation of a line can be written in point-slope form:

$y - y_1 = m(x - x_1)$

where $m$ is the slope and $(x_1, y_1)$ is a point on the line.

In our case, $m = 1$ and $(x_1, y_1) = (4, 5)$.

Substituting these values into the point-slope form, we have:

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

$y - 5 = x - 4$

$y = x - 4 + 5$

$y = x + 1$

3. Final Answer

The equation of the line is $y = x + 1$. The correct answer is (b).