Chapter 8 - Coordinate Geometry and Linear Systems - 8.4 - Writing Equations of Lines - Problem Set 8.4 - Page 360: 2

$3x-7y=1$

Using $y-y_1=m(x-x_1)$ or the Point-Slope Form, the equation of the line with the given point $( 5,2 )$ and slope $m= \dfrac{3}{7} $ is \begin{array}{l}\require{cancel} y-2=\dfrac{3}{7}(x-5) \\\\ 7(y-2)=3(x-5) \\\\ 7y-14=3x-15 \\\\ -3x+7y=-15+14 \\\\ -3x+7y=-1 \\\\ 3x-7y=1 .\end{array}