To find the equation of a line that is parallel to $y = 4x + 9$ and passes through the point $(2,1)$, let's go through the following steps:

1. Identify the Slope of the Parallel Line:

   • Since parallel lines have the same slope, the slope of our new line will also be $4$ (the slope of $y = 4x + 9$).

2. Use the Point-Slope Form:

   • The point-slope form of a line is: $y - y_1 = m(x - x_1)$
   • Here, $m = 4$, $x_1 = 2$, and $y_1 = 1$.

3. Plug in the Values: $y - 1 = 4(x - 2)$

4. Simplify the Equation: $y - 1 = 4x - 8$ $y = 4x - 7$

So, the equation of the line parallel to $y = 4x + 9$ and passing through $(2,1)$ is: $y = 4x - 7$

Answer: Option A: $y = 4x - 7$

Would you like further details or have any questions about this solution?

Here are five related questions to deepen your understanding:

1. How do you find the equation of a line perpendicular to a given line?
2. Why do parallel lines have the same slope?
3. How would you determine the equation of a line passing through two points?
4. How can you convert between point-slope and slope-intercept forms?
5. What changes if the given point through which the line passes is altered?

Tip: Remember, when two lines are parallel, they always share the same slope.