## Intermediate Algebra (12th Edition)

$2x+y=8$
Using $y-y_1=\dfrac{y_1-y_2}{x_1-x_2}(x-x_1)$ or the two-point form of linear equations, the equation of the line passing through $( 5,-2 )$ and $( -3,14 )$ is \begin{array}{l}\require{cancel} y-(-2)=\dfrac{-2-14}{5-(-3)}(x-5) \\\\ y+2=\dfrac{-2-14}{5+3}(x-5) \\\\ y+2=\dfrac{-16}{8}(x-5) \\\\ y+2=-2(x-5) \\\\ y+2=-2x+10 \\\\ 2x+y=10-2 \\\\ 2x+y=8 .\end{array}