SOLUTION: find the equation of the straight line which passes through the point (-2,6) and is:- (a) parallel to the line with equation x=3 (b) perpendicular to the line with equation y +2x

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First there are an infinite number of equations that fit the descriptions not just one, so it is wrong to ask for "the equation".
a)x=3 forms a vertical line.
and we want a line that is parallel.
x=-2
b)
perpendicular to y+2x=0
y=-2x
slope is -2
we want a slope of 1/2 for it to be perpendicular.
first we need to find b in the equation y=mx+b
6=-2*1/2+b
6=-1+b
7=b
y=x/2+7
check
6=-2/2+7
6=6
ok
c)
-2,6
parallel to y - 3x=4
y=3x+4
slope is 3
6=3*-2+b
6=-6+b
12=b
y=3x+12
check
6=-2*3+12
6=6
ok