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 = [tex]\frac{|c_{1} - c_{2}|}{\sqrt{1 + m^{2}}} [/tex]
========================================================
Part (1):
=======
The distance between the lines
Y₁ = 3x + 10 and Y₂ = 3x - 20
∴ m = 3 , c₁ = 10 and c₂ = -20
∴ d = [tex]\frac{| 10 - (-20)|}{\sqrt{1 + 3^{2}}}= \framebox{9.5}[/tex]
========================================================
Part (2):
=======
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 = [tex]\frac{| 1.5- (-5)|}{\sqrt{1 + 1.5^{2}}}= \framebox{3.6}[/tex]
