Final answer:
The equation of the line perpendicular to y = -5x + 1 and passing through the point (-5,1) is y - 1 = 1/5(x + 5).
Step-by-step explanation:
To find the equation of a line perpendicular to y = -5x + 1 and passing through the point (-5,1), we need to determine the slope of the new line first. The slope of a line perpendicular to another line is the negative reciprocal of the original slope.
The original slope is -5, so the slope of the new line is 1/5. Now, we can use the point-slope form of a line to write the equation of the line. Substitute the slope and the coordinates of the point into the equation:
y - y1 = m(x - x1)
where (x1, y1) is the point and m is the slope. Plugging in the values, we get:
y - 1 = 1/5(x + 5)
This is the equation of the line perpendicular to y = -5x + 1 and passing through the point (-5,1).