Find the distance between the lines y=3x+10 y=3x-20 and y=3/2x+3/2 y=3/2x-5

At first we need to know how to find the distance between two parallel lines
The parallel lines which have the same slope 
If we have two parallel lines ⇒ y₁ = mx + c₁   and    y₂ = mx + c₂
So, the distance between y₁ and y₂ = d =
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Part (1):
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The distance between the lines

Y₁ = 3x + 10    and       Y₂ = 3x - 20
∴ m = 3  , c₁ = 10  and  c₂ = -20
∴ d =

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Part (2):
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The distance between the lines

Y₁ = 3/2 x + 3/2    and       Y₂ = 3/2 x - 5
∴ m = 3/2 = 1.5  , c₁ = 3/2 = 1.5   and  c₂ = -5
∴ d =