$$\text { Find an equation of the line through } ( 5,2 ) \text { that is parallel to the line } 4 x + 6 y + 5 = 0 \text {. }$$

Name: \[\text { Find an equation of the line through } ( 5,2 ) \text { that is parallel to the line } 4 x + 6 y + 5 = 0 \text {. }\]
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Question

Quizplus · Accepted Answer

The Answer is First, express

4 x + 6 y + 5 = 0

in the basic form

y = m x + b

\begin{array} { l } 6 y = - 4 x - 5 \y = - \frac { 2 } { 3 } x - \frac { 5 } { 6 } \m = - \frac { 2 } { 3 }\end{array}

Perpendicular lines have negative reciprocal slopes

\begin{array} { l } m = \frac { 3 } { 2 } \2 = \frac { 3 } { 2 } ( 5 ) + b ~~~~~~\quad b = 2 - \frac { 15 } { 2 } = - \frac { 11 } { 2 } \y = \frac { 3 } { 2 } x - \frac { 11 } { 2 }\end{array}

Find an equation of the line through (5,2) that is parallel to the line 4x+6y+5=0. \text { Find an equation of the line through } ( 5,2 ) \text { that is parallel to the line } 4 x + 6 y + 5 = 0 \text {. } Find an equation of the line through (5,2) that is parallel to the line 4x+6y+5=0.

$\text { Find an equation of the line through } ( 5,2 ) \text { that is parallel to the line } 4 x + 6 y + 5 = 0 \text {. }$