Final answer:
To find the equation of a line perpendicular to y = 8x - 5/3 and passing through (5, 5), we use the point-slope form with the negative reciprocal slope of -1/8. The resulting equation is y = (-1/8)x + 45/8.
Step-by-step explanation:
The student is asking to find an equation of a line that is perpendicular to the line y = 8x - 5/3 and that passes through the point (5, 5). The original line has a slope of 8. For a line to be perpendicular, its slope must be the negative reciprocal of the original line's slope. Therefore, the slope of the perpendicular line will be -1/8.
To find the equation of the line, we use 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. Thus, the equation with the point (5, 5) and the slope -1/8 is y - 5 = (-1/8)(x - 5).
Simplifying this equation to y = mx + b form, we have:
y = (-1/8)x + (5 + (1/8)*5) = (-1/8)x + (40/8 + 5/8) = (-1/8)x + 45/8.