How can i look at an equation and determine if it is the same line, intersecting or parallel?

It is simple, if you look at the slope of the 2, if they have the same slope then it means it definitely is not intersecting, and if you look at which points that the equation begins at you can tell if it starts at the same points with the same slope then it is same line, if it starts at different points with same slope then it is parallel lines

the coordinates of a' are (-5, 10)

what i did is i   turned 2 1/2 into an improper fraction which is 5/2. then i multiplied this (the scale factor) by the coordinates of a which is (-2,4).

hope this : )