Question

Find distance between parallel lines y=x+3 and y=x-2

Answer 1

We were given the lines

$y=x+3$

and

$y=x-2$

The distance between the two parallel lines is given by the formula,

$d=\frac{|b_2-b_1|}{\sqrt{m ^{2}+1 } }$

Where

$b_1=3$, the y intercept of the first line

$b_2=-2$, the y intercept of the second line

and

$m=1$, the slope of the lines

$d=\frac{|-2-3|}{\sqrt{1 ^{2}+1 } }$

$d=\frac{|-5|}{\sqrt{1 +1 } }$

$d=\frac{5}{\sqrt{2} }$

$d=\frac{5\sqrt{2}}{2}$

Therefore the distance between the two lines is approximately 3.5 units to the nearest tenth