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{\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{\sqrt{1 ^(2)+1 } }`


`d=(|-5|)/(√(1 +1 ) )`


`d=(5)/(√(2) )`


`d=(5√(2))/(2)`

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