Find the point on the line 7x+5y−8=0 which is closest to the point (−1,−1).
y = -7/5 x + 8/5
the shortest line from (-1,-1) has a slope of
... 5/7
... it is perpendicular to the given line
point-slope ... y + 1 = 5/7 (x + 1)
... y = 5/7 x - 2/7
the intersection of the two lines is the closest point