Parallel lines

Question

prove algebraically that lines x - 10y = 4 and -1/2 x + 5y = 0 are parallel

Answer 1

x-10y=4

(-1/2)x+5y=0

first equation:

x-10y=4

-10y=-x+4

10y=x-4

y=(1/10)x-4/10

y=(1/10)x-(2/5) (the slope is 1/10)

second equation:

(-1/2)x+5y=0

5y=(1/2)x

divide both sides by 5

y=[(1/2)/5]x

y=(1/10)x (the slope is 1/10)

if two lines have the same slope then they are parallel