To find the equation of a line parallel to another line, we need to use the fact that parallel lines have the same slope. The given line has the equation 6x - 5y - 3 = 0, which we can rearrange to solve for y:
6x - 5y - 3 = 0
-5y = -6x + 3
y = (6/5)x - 3/5
The slope of this line is 6/5, so any line parallel to it will also have a slope of 6/5. We can use the point-slope form of the equation of a line to write the equation of the line passing through (-7,7) with this slope:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the point (-7,7):
y - 7 = (6/5)(x - (-7))
Simplifying, we get:
y - 7 = (6/5)x + 42/5
y = (6/5)x + 42/5 + 7
y = (6/5)x + 77/5
Therefore, the equation of the line passing through (-7,7) and parallel to the line 6x - 5y - 3 = 0 is y = (6/5)x + 77/5.