The problem asks to write the equation of a line that is parallel to $y = 4x - 1$ and passes through the point $(2, 3)$.

Step-by-Step Solution:

1. Identify the slope of the given line:

   • The given line is $y = 4x - 1$, which is in slope-intercept form $y = mx + b$, where $m$ is the slope.
   • Here, $m = 4$, so the slope of the line parallel to this will also be $4$, because parallel lines have the same slope.

2. Use the point-slope form to find the equation: The point-slope form of a line is: $y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is a point on the line, and $m$ is the slope. We know the line passes through $(2, 3)$, and the slope is $4$.

   Substituting these values: $y - 3 = 4(x - 2)$

3. Simplify the equation: Expand and simplify: $y - 3 = 4x - 8$ $y = 4x - 8 + 3$ $y = 4x - 5$

So, the equation of the line is $y = 4x - 5$.

Answer:

The correct option is A. $y = 4x - 5$.

Would you like a detailed breakdown of the steps, or do you have any questions?

Here are 5 related questions to explore:

1. How would you find the equation of a line perpendicular to $y = 4x - 1$?
2. What is the relationship between the slopes of parallel lines?
3. Can you write the equation of a line passing through two given points?
4. How do you convert a line equation from point-slope form to slope-intercept form?
5. What happens to the slope if two lines are perpendicular?

Tip: Always remember, parallel lines have identical slopes while perpendicular lines have slopes that are negative reciprocals of each other.