Solve the following problems and illustrate your answer. Explain for better understanding. If a linear space consists of 6 points and each point is connected by a unique line to every other point, how many total lines are there in the space Provide the illustration and calculation method.

Gordon borrowed $420 from Lyn and agreed to pay her back $24 every month. Write a formula (linear model) showing the amount of money Gordon still owes at any time. Clearly define your variables.

a and b are two points in the third dimension. Write an equation that describes the set of points that are equidistant to a and b. Draw a picture of this set in the case where a = i and b = j.

A contest has prize winnings that total $5,000. If each entrant pays a $20 fee, write a graph linear equation that can represent the money generated from the contest. If there are 600 entrants to the contest, how much money did they generate?