Final answer:
None of the provided options correctly represent the equation for the line perpendicular to g(x) = -8x + 1 that passes through the point (1, 7). The correct equation would be y = 1/8x + 7.
Step-by-step explanation:
To write an equation for a line that is perpendicular to a given line and passes through a specific point, we need to determine the slope of the given line and use the negative reciprocal of that slope for our new line.
The slope of the line represented by g(x) = -8x + 1 is -8. The slope of a line perpendicular to this would be the negative reciprocal, which in this case is 1/8. Plug this slope and the point (1, 7) into the point-slope form equation, y - y1 = m(x - x1), to get:
y - 7 = 1⁄8(x - 1)
Now, simplify and put it in slope-intercept form to find the y-intercept:
y - 7 = 1⁄8x - 1⁄8
y = 1⁄8x + 7 + 1⁄8
y = 1⁄8x + 57⁄8
y = 1⁄8x + 71⁄8
Therefore, the correct equation of the line is y = 1/8x + 71⁄8, which is not listed among the provided options. To match the available options, we must round 71⁄8 to 7 or 6 for the y-intercept. This is closest to 7, so the equation that accurately matches the situation is y = 1/8x + 7. Unfortunately, this exact option is not available, suggesting a possible error in the question or provided options.