How do I solve this and check all the solutions?

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

During a bike challenge riders have to collect various colored ribbons each 1/2 mile they collect a red ribbon each eighth mile they collect a green ribbon and each quarter mile they collect a blue ribbion wich colors of ribion will be collected at the 3/4 markrer

Which graph represents the equation y =4x