prove the lines are parallel

Question

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

Answer 1

Write each equation in slope- intercept form. If the slopes are the same and they have different y-intercepts, they are parallel. Y=1/10 x - 4/10 y= 1/10 x + 0 They are parallel, both have 1/10 as their slope and a different y-intercept.

Answer 2

Parallel lines mean that they both contain the same slope.

x - 10y = 4 

^-1/₂x + 5y = 0

 

What we need to do is isolate y in each case:

x - 10y = 4

-10y = -x + 4

y = ^-x/_-10 - ⁴/₁₀

y = ¹/₁₀x - ²/₅

 

^-1/₂x + 5y = 0

5y = ¹/₂x

y = ¹/₂x / 5

y = ¹/₁₀x

 

Both problems have the exact same slope (1/10), so both lines are parallel.