# Chapter 10 - Section 10.2 - Arithmetic Sequences - Exercise Set - Page 1060: 57

$f(x)=-\dfrac{x}{4}+\dfrac{5}{4}$

#### Work Step by Step

We need to find the line equation by using two points such as: $(1,1); (2,-3)$ $\dfrac{y-1}{-3-1}=\dfrac{x-1}{2-1}$ This gives: $y-1= -4x+4$ or, $x=\dfrac{-y+5}{4}=-\dfrac{y}{4}+\dfrac{5}{4}$ Thus, we have the linear equation for the function $f(x)$ is $f(x)=-\dfrac{x}{4}+\dfrac{5}{4}$

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