It is a straight line.
standard form is y = mx + b where m = slope
3x - 6y = 12
6y = 3x -12
y = .5x -2
any other line with slope = 0.5 would be parallel to it
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q2
If you mean -x+y = 12 then y = x+12 and so the parallel line will have the same slope but with a different y intercept.
4x+y = 14 will be parallel to the above equation because the slope or gradient remains the same but the y intercept changes.
y = -7x + 6 is the equation of a straight line. It has a slope of '-7' and a y-intercept of '6'. For it to be parallel it must be compared to another line. e.g. y = -7x + 12 is a paralle line However, y = 7x + 6 is NOT a parallel line, because the slope is in a different direction.
The second equation works out as y = -1/2x+6 therefore it is perpendicular