Final answer:
The equation of the line parallel to y = -2/7x + 9 and passing through (7, -1) is y = -2/7x + 1.
Step-by-step explanation:
To find the equation of a line that is parallel to the line y = -2/7x + 9 and passes through the point (7, -1), we can use the fact that parallel lines have the same slope. The given line has a slope of -2/7, so the parallel line will also have a slope of -2/7. Using the point-slope equation, we can write the equation of the line as:
y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Substituting the values, we get:
y - (-1) = -2/7(x - 7)
y + 1 = -2/7x + 14/7
y = -2/7x + 14/7 - 1
y = -2/7x + 7/7
y = -2/7x + 1