Final answer:
The equation of a line parallel to y = -2/7x + 1 and passing through the point (-7, 3) is found using the slope -2/7 and point-slope form, resulting in the equation C. y = (-2/7)x + 17/7.
Step-by-step explanation:
To determine the equation of a line parallel to y = -2/7x + 1 and passing through the point (-7, 3), we must use the given slope and the coordinates of the point to find the y-intercept of the new line.
Since parallel lines have the same slope, we will keep the slope of -2/7.
Now, we use the point-slope form of the line equation y - y1 = m(x - x1), where (x1, y1) is the point the line passes through, and m is the slope, to plug in our values:
y - 3 = -2/7(x + 7)
Multiplying both sides by 7 to eliminate the fraction and simplify:
7y - 21 = -2x - 14
To put it in slope-intercept form (y = mx + b), we solve for y:
y = (-2/7)x + 17/7
Therefore, the correct equation is C. y = (-2/7)x + 17/7.