The problem asks us 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

The problem asks us 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

First, we need to find the slope of the given line $y = x - 1$. The slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In the given line $y = x - 1$, the slope $m = 1$.

Since we are looking for a line parallel to $y = x - 1$, the slope of the new line will be the same as the slope of the given line. Thus, the slope of the new line is also $m = 1$.

Now we know the slope $m = 1$ and a point $(4, 5)$ that the line passes through. We can use the point-slope form of a linear equation, which is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope.

Plugging in the values, we get $y - 5 = 1(x - 4)$.

Simplifying the equation, we have:

$y - 5 = x - 4$

$y = x - 4 + 5$

$y = x + 1$

3. Final Answer

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