Final answer:
To find the equation of the line perpendicular to y=4x that passes through the point (−8,5), we use the slope −1/4 which is the negative reciprocal of 4, and the point-slope form to obtain the equation y = −1/4x + 3.
Step-by-step explanation:
The correct equation of the line that passes through (−8,5) and is perpendicular to y=4x can be found by understanding that perpendicular lines have slopes that are negative reciprocals of each other. Given the slope of the original line is 4, the slope of the perpendicular line will be −1/4. Therefore, to find the equation of the line, we apply the point-slope form, which is y − y1 = m(x − x1), where (x1, y1) is the point the line passes through and m is the slope. Substituting the given point and the slope of the perpendicular line, we get y − 5 = −1/4(x + 8). Simplifying this equation, we find y − 5 = −1/4x − 2 and then y = −1/4x + 3 as the final equation of the perpendicular line.