To solve this problem, we need to find the equation of a line that is parallel to the line $y = 4x + 9$ and passes through the point $(2, 1)$.

Step 1: Identify the slope of the given line

The slope-intercept form of a line is given by: $y = mx + c$ where $m$ is the slope and $c$ is the y-intercept.

For the line $y = 4x + 9$, the slope $m$ is 4.

Step 2: Use the point-slope form of the line equation

The point-slope form of a line's equation is: $y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope.

Substituting the point $(2, 1)$ and the slope $m = 4$: $y - 1 = 4(x - 2)$

Step 3: Simplify the equation

Expand and simplify the equation: $y - 1 = 4x - 8$ $y = 4x - 7$

Step 4: Identify the correct answer

The equation of the line is $y = 4x - 7$, which corresponds to option A.

Final Answer:

The correct answer is A: $y = 4x - 7$.

Would you like to go over any details or have further questions?

Here are some related questions for practice:

1. How do you find the equation of a line that is perpendicular to $y = 4x + 9$ and passes through $(2, 1)$?
2. What is the slope of a line parallel to $y = -3x + 5$?
3. How do you determine if two lines are parallel or perpendicular given their equations?
4. What is the general form of a linear equation?
5. How can you find the y-intercept of a line given its equation?

Tip: Remember that parallel lines always have the same slope, but different y-intercepts.