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**http://math.sfsu.edu/federico/Clase/Math350.S15/linea.JPG [Broken] 1. Homework Statement**

The picture below represents the map from a "green projective line" to a "red projective line." It takes the "green points" 1,3,7,-11 to the "red points" 0,6,10,20, respectively as shown by the ruler. Let f be the corresponding linear fractional, so f(1) = 0, f(3) = 6, f(7) = 10, f(-11) = 20. Find a formula for the "red point" f(x) on the ruler where the "green point" x lands.

## Homework Equations

a linear fractional is where f(x) = (ax+b)/(cx+d) where ad-bc is not equal to 0.

## The Attempt at a Solution

First a did a system of equations:

(a(1) + b) / ( c(1) + d ) = 0

(a(3) +b) / ( c(3) + d )= 6

(a(7) +b) / ( c(7) + d ) = 10

(a(-11) +b) / (c(-11) + d )= 20

Thinking I could solve for a,b,c,d. However if I get all the letters in terms of let's say d and solve, this becomes nonsensical, since something d over something d is a number (the d's reduce) , and I'm left with a number = another number.

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