posted by Rudy .
Write an equation of the line that passes through the point (i) parallel to the given value, and (ii) perpendicular to the given line.
The given line is -5x - 5y = 90
or , dividing by -5
x+y = -18
since the new line is parallel to it, its equation differs only in the costant, so let the new equation be
x+y = c , but (7,1) lies on it, so
7+1=c = 8
If perpendicular, then the slop must be negative reciprocal : -1 ----> 1/1 = 1
x-y = k
but (7,1) on it, so
7-1 = k = 6
x - y = 6