Answer
$y-4=-3(x-1)$
Work Step by Step
Using the properties of equality, the given linear equation, $
3x+y=5
$ is equivalent to
\begin{array}{l}
y=-3x+5
.\end{array}
Using $y=mx+b$ or the Slope-Intercept form where $m$ is the slope, then the slope of the given line is $
-3
$. Since parallel lines have the same slope, then the needed linear equation has the same slope and it passes through the given point $(
1,4
)$. Using $y-y_1=m(x-x_1)$ or the Point-Slope form where $m$ is the slope and $(x_1,y_1)$ is a point on the line, then the equation of the needed line is
\begin{array}{l}
y-4=-3(x-1)
.\end{array}
