Find the equation of the line passing through the point $(4, 5)$ and parallel to the line $y = x - 1$.

1. Problem Description

Find the equation of the line passing through the point $(4, 5)$ and parallel to the line $y = x - 1$.

2. Solution Steps

The equation of a line is given by $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Parallel lines have the same slope. The given line $y = x - 1$ has a slope of $1$.

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

So the equation of the line we are looking for is $y = 1x + b$, or $y = x + b$.

We know that the line passes through the point $(4, 5)$. Substituting these values into the equation, we get:

$5 = 4 + b$

Subtracting $4$ from both sides, we get:

$b = 5 - 4 = 1$

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

3. Final Answer

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