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

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 $y = x - 1$. We need to choose the correct answer from the given options.

2. Solution Steps

The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Since the line we are looking for is parallel to $y = x - 1$, it has the same slope. The slope of $y = x - 1$ is $1$.

So the equation of our line is $y = 1x + b$, or $y = x + b$.

Now we need to find the value of $b$. We know that the line passes through the point $(4, 5)$. We can plug these coordinates into the equation $y = x + b$ to solve for $b$.

$5 = 4 + b$

$b = 5 - 4$

$b = 1$

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

3. Final Answer

(b) $y = x + 1$