Question

Find the distance between the lines Y=3x+10 Y=3x-20 AND Y=3/2x+3/2 Y=3/2x-5

Answer 1

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 = $\frac{|c_{1} - c_{2}|}{\sqrt{1 + m^{2}}}$
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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 = $\frac{| 10 - (-20)|}{\sqrt{1 + 3^{2}}}= \framebox{9.5}$

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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 = $\frac{| 1.5- (-5)|}{\sqrt{1 + 1.5^{2}}}= \framebox{3.6}$