Final answer:
The equation of the line parallel to y - 9x + 8 and passing through the point (-7, 4) is y = 9x + 67, which does not match any of the given options.
Step-by-step explanation:
To find the equation of a line that is parallel to a given line and passes through a specific point, one must first understand that parallel lines have the same slope. The given line is y - 9x + 8, which can be rearranged to slope-intercept form (y = mx + b) to identify the slope (m). This form allows us to see that the slope of the original line is 9. Because parallel lines share the same slope, our new line will also have a slope of 9.
Given the point (-7, 4) through which our new line must pass, we use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope. Substituting the given point and the slope, we get:
y - 4 = 9(x + 7)
Broadening the expression, we obtain:
y - 4 = 9x + 63
Finally, adding 4 to both sides gives us:
y = 9x + 67
Hence the equation of the line parallel to the given line and passing through the point (-7, 4) is y = 9x + 67, which is not one of the provided options. Therefore, it seems there might be a typo or error in the options given.