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

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2022-10-03
Answered

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

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typeOccutfg

Answered 2022-10-04
Author has **6** answers

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,

$a{x}_{0}+b{y}_{0}+c\prime =0,\phantom{\rule{1ex}{0ex}}\text{giving,}\phantom{\rule{1ex}{0ex}}c\prime =-a{x}_{0}-b{y}_{0}.$

$\therefore {l}_{2}:ax+by=a{x}_{0}+b{y}_{0}.$

${l}_{1}:ax+by+c=0$ 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,

$a{x}_{0}+b{y}_{0}+c\prime =0,\phantom{\rule{1ex}{0ex}}\text{giving,}\phantom{\rule{1ex}{0ex}}c\prime =-a{x}_{0}-b{y}_{0}.$

$\therefore {l}_{2}:ax+by=a{x}_{0}+b{y}_{0}.$

kasibug1v

Answered 2022-10-05
Author has **4** answers

Accordingly, the eqn. of the reqd. line is given by,

$3x-2y=3\left(1\right)-2\left(6\right)\Rightarrow 3x-2y+9=0.$

$3x-2y=3\left(1\right)-2\left(6\right)\Rightarrow 3x-2y+9=0.$

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