Final answer:
The equation of the line parallel to y = 4x + 1 and passing through the point (1, 1) is y = 4x - 3.
Step-by-step explanation:
To find the equation of a line that is parallel to the given line y = 4x + 1 and passes through the point (1, 1), we will use the fact that parallel lines have the same slope. The slope of the given line is 4.
Since the desired line must be parallel, it will also have a slope of 4. The point-slope form of a line's equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting the point (1, 1) and the slope 4, we get:
y - 1 = 4(x - 1)
Expanding and simplifying, we have:
y - 1 = 4x - 4
y = 4x - 3
Therefore, the equation of the line that is parallel to y = 4x + 1 and passes through the point (1, 1) is y = 4x - 3.