Final answer:
The equation of the line parallel to y = x + 5 and passing through (8, 1) is y = x - 7. We use the point-slope formula considering the same slope as the given line, which leads to the answer option a.
Step-by-step explanation:
The student's question is asking to write the equation of a line that is parallel to the given line y = x + 5 and that passes through the point (8, 1). A line parallel to another has the same slope but a different y-intercept. Since the original line has a slope of 1 (as seen from the coefficient of x), the parallel line must also have a slope of 1. To find the equation of the new line, we use the point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is the point given and m is the slope. Plugging in our values, we get y - 1 = 1*(x - 8), simplifying this, we get y = x - 8 + 1, which simplifies further to y = x - 7. So, the correct answer is option a: y = x - 7.