Question

How can you tell if an equation's line, if done on a graph, is parallel/perpendicular/same line..?

Answer 1

the slope intercept form of a line is

y = mx + b

m = slope and b = y-intercept

when 2 or more lines have the same slope they are parallel

y = 2x

y = 2x - 10

m = 2 for both lines

perpendicular the slopes multiply to give -1

y = 3x

y = -1/3 x + 11

-1/3 * 3 = -1

so perpendicular

Answer 2

same line, have the same slope and same intercept

y = 4x + 6

and

3y = 12x + 18

divide the 2nd line by 3 and you get the 1st line