# Chapter 3 - Review - Page 197: 95

$f(x)=\dfrac{3}{4}x+\dfrac{7}{2}$

#### Work Step by Step

Using the properties of equality, the given equation, $4x+3y=5 ,$ is equivalent to \begin{array}{l} 3y=-4x+5 \\\\ y=-\dfrac{4}{3}x+\dfrac{5}{3} .\end{array} Using $y=mx+b$, where $m$ is the slope, the slope of the given line is \begin{array}{l} m=-\dfrac{4}{3} .\end{array} Using $m= \dfrac{3}{4}$ (negative reciprocal slope since the lines are perpendicular) and the given point $( -6,-1 ),$ then the equation of the line is \begin{array}{l} y-(-1)=\dfrac{3}{4}(x-(-6)) \\\\ y+1=\dfrac{3}{4}(x+6) \\\\ y+1=\dfrac{3}{4}x+\dfrac{18}{4} \\\\ y=\dfrac{3}{4}x+\dfrac{18}{4}-1 \\\\ y=\dfrac{3}{4}x+\dfrac{18}{4}-\dfrac{4}{4} \\\\ y=\dfrac{3}{4}x+\dfrac{14}{4} \\\\ y=\dfrac{3}{4}x+\dfrac{7}{2} .\end{array} In function notation, this is equivalent to $f(x)=\dfrac{3}{4}x+\dfrac{7}{2} .$

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