Final answer:
To find the equation of a line parallel to y = -54x + 1 and passing through (4, 1), we need to use the fact that parallel lines have the same slope. The equation of the line is y = -54x + 217.
Step-by-step explanation:
To find the equation of a line parallel to y = -54x + 1 and passing through (4, 1), we need to use the fact that parallel lines have the same slope. The given line has a slope of -54. So, the equation of the parallel line will also have a slope of -54. Using the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the point (4, 1), we can substitute the values to find the equation.
Using the point-slope form, the equation becomes: y - 1 = -54(x - 4)
Simplifying the equation, we get: y - 1 = -54x + 216
Finally, rearranging the equation in slope-intercept form (y = mx + b) gives us the equation of the line passing through (4, 1) and parallel to y = -54x + 1 as y = -54x + 217.