Question 63097
(A) Equation of the given line is -2x + y = 9
In the slope intercept form the above equation can be written as y = 2x + 9
Slope of this line = 2

So slope of any line parallel to this line = 2 as parallel lines have equal slopes.

The required line has a slope of 2 and passes through (-1,6)

The equation is y - 6 = 2(x - (-1))
==>             y - 6 = 2(x+1)
==>             y - 6 =2x + 2
==>             y - 6 + 6 = 2x + 2 + 6
==>             y = 2x + 8 is the required equation.

(B)  The given line is 2x + y = 9
THis is rewritten as y = - 2x + 9
Slope of this line = -2

[as product of slopes of perpendicular lines = -1]

 slope of the perpendicular line = -1/-2  
                                  = 1/2
The required line passes through (-1, 6)

The required equation is y - 6 = 1/2 (x + 1)

==> 2(y-6) = 1(x + 1)
==> 2y - 12 = x + 1
==> 2y - 12 - x - 1 = 0
==> -x + 2y - 13 = 0



Good Luck!!!