# Determine the equation of the line parallel to 3x - 2y + 4 = 0 and passing through (1,6)

Determine the equation of the line parallel to 3x - 2y + 4 = 0 and passing through (1,6)
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typeOccutfg
Recall that the eqn. of a line parallel to the given line
${l}_{1}:ax+by+c=0$ is of the Form ${l}_{2}:ax+by+c\prime =0,c\prime \ne c.$
If we compare the slopes of the lines ${l}_{1}\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}{l}_{2}$, we will find that
the result is quite obvious. If, in addition, #(x_0,y_0) in l_2, then,
$a{x}_{0}+b{y}_{0}+c\prime =0,\phantom{\rule{1ex}{0ex}}\text{giving,}\phantom{\rule{1ex}{0ex}}c\prime =-a{x}_{0}-b{y}_{0}.$
$\therefore {l}_{2}:ax+by=a{x}_{0}+b{y}_{0}.$
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kasibug1v
Accordingly, the eqn. of the reqd. line is given by,
$3x-2y=3\left(1\right)-2\left(6\right)⇒3x-2y+9=0.$