Question

If given an equation of a line such as y = (-1/2)x + 6, demonstrate how to create an equation of a line parallel and perpendicular to this line that goes through another point such as (4, 10).

Answer 1

If line
`y_(1)=m_(1)x+b_(1)` is parallel to line
`y_(2)=m_(2)x+b_(2)` i.e
`y_(1) \parallel y_(2)` then, by definition,
`m_(2)=m_(1)`. Taking this along with the given point
`(h,y)` a line can be constructed in point slope form that satisfies the requirements as
`y_(2)-k=m_(2)(x-h)`.

Similarly, If line
`y_(1)=m_(1)x+b_(1)` is perpendicular to line
`y_(2)=m_(2)x+b_(2)` i.e
`y_(1) \perp y_(2)` then, by definition,
. Taking this along with the given point
`(h,y)` a line can be constructed in point slope form that satisfies the requirements as
`y_(2)-k=m_(2)(x-h)`. .