MHB Solving for U & P in a Coordinate Change

[avyunker]

Assume that you are given a coordinate change on a line which changes the coordinate x to a new coordinate z given by the formula z=U⋅x+P where U,P are real numbers with U non zero. If the new coordinate of the point -13 is 12 and the new coordinate of the point -7 is 6 then we must have U= ? and P= ? . Moreover, for the same transformation, if the new coordinate is (11) then the original coordinate must have been ?

 

[Greg]

You can use the given information to set up a system of equations:

$$-13U+P=12$$

$$-7U+P=6$$