Question

Find the distance between each pair of parallel lines with the given equationsY = -3/2x + 4 and y = -3/2x - 1 (system)

Answer 1

Rewriting the equations we get

$y=-\frac{3}{2}x+4\Rightarrow2y+3x=8,y=-\frac{3}{2}x-1\Rightarrow2y+3x-2$

We know that distance between two parallel lines of the form

$ax+by=c_1,ax+by=c_2$

is

$d=\frac{c_1-c_2}{\sqrt[]{a^2+b^2}}$

Here

$a=3,b=2,c_1=8,c_2=-2$

Thus the distance d will be

$d=\frac{8-(-2)}{\sqrt[]{9+4}}=\frac{10}{\sqrt[]{13}}$