Question

Find the distance between the pair of parallel lines, y = -2x+1 & y = -2x+16.

Answer 1

$Given \ the \ equations \ of \ two \ non-vertical \ parallel \ lines:\\\\y = mx+b_1\\y = mx+b_2\\\\the \ distance \ between \ them \ can \ be \ expressed \ as : \\\\d= \frac{|b_{1}-b_{2}|}{ \sqrt{ m^2+1} }$

$y = -2x+1\\y = -2x+16 \\\\\\d= \frac{|b_{1}-b_{2}|}{ \sqrt{ m^2+1} } =\frac{| 1-16|}{ \sqrt{ (-2)^2+1} } =\frac{| -15|}{ \sqrt{ 4+1} } =\frac{15}{\sqrt{5}}\cdot \frac{\sqrt{5}}{\sqrt{5}}=\\ \\\\=\frac{15\sqrt{5}}{5}=3\sqrt{5}\approx 3\cdot 2.24 \approx 6.72$