We were given the lines
[tex]y=x+3[/tex]
and
[tex]y=x-2[/tex]
The distance between the two parallel lines is given by the formula,
[tex]d=\frac{|b_2-b_1|}{\sqrt{m ^{2}+1 } }[/tex]
Where
[tex]b_1=3[/tex], the y intercept of the first line
[tex]b_2=-2[/tex], the y intercept of the second line
and
[tex]m=1[/tex], the slope of the lines
[tex]d=\frac{|-2-3|}{\sqrt{1 ^{2}+1 } }[/tex]
[tex]d=\frac{|-5|}{\sqrt{1 +1 } }[/tex]
[tex]d=\frac{5}{\sqrt{2} }[/tex]
[tex]d=\frac{5\sqrt{2}}{2}[/tex]
Therefore the distance between the two lines is approximately 3.5 units to the nearest tenth
