1. The line 3y = - 4x + 2 can be written as y = -4/3 x + 2/3It is in the form y = mx + bslope of the given line m = -4/3So the slope of the perpendicular line will be = - 1/m = -1/(-4/3) = 3/4 2. Line s is represented by the equation y=-2x+3.....................slope = -2 = mParallel to line a : y = -2x + 5...............................................Same slope = -2 = mPerpendicular to line a : y = 1/2 x + 7....................................slope = 1/2 = -1/mNeither parallel nor perpendicular to line a : y=2x - 1..................slope = 2 is not equal to m or -1/m3. By rewriting 2x +5y = 10 into slope intercept form y=mx+b : y = -2/5 x + 2As slope is m= -2/5, the slope of the parallel line must be same and = -2/5So substituting value of coordinates of the point ( 5,-4) in y=mx+b :-4 = (-2/5)*5 + b or b = -2Therefore the line y = (-2/5)*x - 2 is the line that passes through (5,-4) and parallel to 2x+5y=104. the line is in slope intercept form y=mx+b : y =x/3 - 1 As slope is m= 1/3, the slope of the perpendicular line must be -1/m = -1/(1/3) = -3 So substituting value of coordinates of the point ( 4,2) in y=mx+b : 2 = (-3)*4 + b or b = 14The required perpendicular line is y = -3x +14 5. Slope of line through (x1,y1) and (x2,y2) is m= (y2-y1)/(x2-x1)Slope line1 is (0-a)/ (b-0) = -a/bSlope line2 is (-d-0)/ [0-(-c)] = -d/cTo both the lines be parallel : slopes of both line s must be equalSo -a/b = -d/c is true in order to conclude that the lines are parallel.