Example

Consider the parallel lines [latex]d_1[/latex] and [latex]d_2[/latex] :

Therefore: d([latex]d_1[/latex], [latex]d_2[/latex]) = 2 In the Cartesian plane, if [latex]d_1[/latex] has the equation "y = mx + b" and if [latex]d_2[/latex] has the equation "y = mx + b'", with b ≥ b', then:

[latex]\textrm{m}\space\overline{\textrm{AB}}=\dfrac{\textrm{b}-\textrm{b'}}{\sqrt{\textrm{m}^2+1}}[/latex].

Therefore, if [latex]d_1[/latex] has the equation "y = 3x + 8" and if [latex]d_2[/latex] has the equation "y = 3x + 4", then:

[latex]\textrm{m}\space\overline{\textrm{AB}}=\dfrac{\textrm{8}-\textrm{4}}{\sqrt{\textrm{3}^2+1}}[/latex].